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NCERT Textbook
INTEGRALS

Class 12
Maths :-NCERT Solutions - Integrals

Page No 299:
Question 1:

Find the integral of sin 2x


Answer

Page No 299:
Question 2:

Find the anti derivative  (or integral) of Cos 3x


Answer

Page No 299:
Question 3:

 Find the anti derivative  (or integral) of e2x


Answer

Page No 299:
Question 4:

find Integral of  


Answer

Page No 299:
Question 5:

Find the anti derivative  (or integral) of 


Answer

Page No 299:
Question 6:

Find the anti derivative  (or integral) of 


Answer

Page No 299:
Question 7:

Find the anti derivative  (or integral) of 


Answer

Page No 299:
Question 9:

Find the anti derivative  (or integral) of


Answer

Page No 299:
Question 10:

find 


Answer

Page No 299:
Question 11:

find 


Answer

Page No 299:
Question 12:

find 


Answer

Page No 299:
Question 13:

find 


Answer

Page No 299:
Question 14:

find 


Answer

Page No 299:
Question 15:

find 


Answer

Page No 299:
Question 16:

find 


Answer

Page No 299:
Question 17:

find 


Answer

Page No 299:
Question 18:

find 


Answer

Page No 299:
Question 19:

find 


Answer

Page No 299:
Question 20:

find 


Answer

Page No 304:
Question 1:

find Integral of  


Answer

Page No 304:
Question 2:

find Integral of  


Answer

Page No 304:
Question 3:

find Integral of  


Answer

Page No 304:
Question 4:

find Integral of  sin x ⋅ sin (cos x)


Answer

Page No 304:
Question 5:

find Integral of  


Answer

Page No 304:
Question 6:

find Integral of  


Answer

Page No 304:
Question 7:

find Integral of  


Answer

Page No 304:
Question 8:

find Integral of  


Answer

Page No 304:
Question 9:

find Integral of  


Answer

Page No 304:
Question 10:

find Integral of  


Answer

Page No 304:
Question 11:

find Integral of  


Answer

Page No 304:
Question 12:

find Integral of  


Answer

Page No 304:

Question 13:

find Integral of  


Answer

Page No 304:
Question 14:

find Integral of  


Answer

Page No 304:
Question 15:

find Integral of  


Answer

Page No 304:
Question 16:

find Integral of  


Answer

Page No 304:
Question 17:

find Integral of  


Answer

Page No 305:
Question 18:

find Integral of  


Answer

Page No 305:
Question 19:

find Integral of  


Answer

Page No 305:
Question 20:

find Integral of  


Answer

Page No 305:
Question 21:

Find the integral of 


Answer

Page No 305:
Question 22:

Find integral of 


Answer

Page No 305:
Question 23:

Find integral of 


Answer

Page No 305:
Question 24:

Find integral of 


Answer

Page No 305:
Question 25:

Find integral of 


Answer

Page No 305:
Question 26:

Find integral of 


Answer

Page No 305:
Question 27:

Find integral of 


Answer

Page No 305:
Question 28:

Find integral of 


Answer

Page No 305:
Question 29:

 find Integral of  cot x log sin x


Answer

Page No 305:
Question 30:

 find Integral of  


Answer

Page No 305:
Question 31:

 find Integral of  


Answer

Page No 305:
Question 32:

find integral of   


Answer

Page No 305:
Question 33:

find Integral of  


Answer

Page No 305:
Question 34:

find Integral of  


Answer

Page No 305:
Question 35:

find Integral of  


Answer

Page No 305:
Question 36:

find Integral of  


Answer

Page No 305:
Question 37:

find Integral of  


Answer

Page No 307:
Question 1:

find Integral of  


Answer

Page No 307:
Question 2:

find Integral of  


Answer

Page No 307:
Question 3:

find Integral of  cos 2x cos 4x cos 6x


Answer

Page No 307:
Question 4:

find Integral of  sin3 (2x + 1)


Answer

Page No 307:
Question 5:

find Integral of  sin3 x cos3 x


Answer

Page No 307:
Question 6:

find Integral of  sin x sin 2x sin 3x


Answer

Page No 307:
Question 7:

Find the anti derivative  (or integral) of

sin 4x sin 8x


Answer

Page No 307:
Question 8:

find Integral of  


Answer

Page No 307:
Question 9:

find Integral of  


Answer

Page No 307:
Question 10:

find Integral of  sin4 x


Answer

Page No 307:
Question 11:

find Integral of  cos4 2x


Answer

Page No 307:
Question 12:

find Integral of  


Answer

Page No 307:
Question 13:

find Integral of  


Answer

Page No 307:
Question 14:

find Integral of  


Answer

Page No 307:
Question 15:

find Integral of   


Answer

Page No 307:
Question 16:

find Integral of  tan4x


Answer

Page No 307:
Question 17:
find Integral of  


Answer

Page No 307:
Question 18:

find Integral of  


Answer

Page No 307:
Question 19:

Find the anti derivative  (or integral) of


Answer

Page No 307:
Question 20:

find Integral of  


Answer

Page No 307:
Question 22:

find Integral of  


Answer

Page No 315:
Question 1:

find Integral of  


Answer

Page No 315:
Question 2:

find Integral of 


Answer

Page No 315:
Question 3:

find Integral of 


Answer

Page No 315:
Question 4:

find Integral of  


Answer

Page No 315:
Question 5:

find Integral of  


Answer

Page No 315:
Question 6:

find Integral of  


Answer

Page No 315:
Question 7:

find Integral of  


Answer

Page No 315:
Question 8:

find Integral of  


Answer

Page No 315:
Question 9:

find Integral of  


Answer

Page No 316:
Question 10:

find Integral of  


Answer

Page No 316:
Question 11

Find the anti derivative  (or integral) of



Answer

Page No 316:
Question 12:

find Integral of  


Answer

Page No 316:
Question 13:

find Integral of  


Answer

Page No 316:
Question 14:

find Integral of  


Answer

Page No 316:
Question 15:

find Integral of  


Answer

Page No 316:
Question 16:

find Integral of  


Answer

Page No 316:
Question 17:

find Integral of  


Answer

Page No 316:
Question 18:

find Integral of  


Answer

Page No 316:
Question 19:

find Integral of  


Answer

Page No 316:
Question 20:

find Integral of  


Answer

Page No 316:
Question 21:

find Integral of  


Answer

Page No 316:
Question 22:

find Integral of  


Answer

Page No 316:
Question 23:

find Integral of  


Answer

Page No 322:
Question 1:

find Integral of  


Answer

Page No 322:
Question 2:

find Integral of  


Answer

Page No 322:
Question 3:

find Integral of  


Answer

Page No 322:
Question 4:

find Integral of  


Answer

Page No 322:
Question 5:

find Integral of  


Answer

Page No 322:
Question 6:

find Integral of  


Answer

Page No 322:
Question 7:

find Integral of  


Answer

Page No 322:
Question 8:

find Integral of  


Answer

Page No 322:
Question 9:

find Integral of  


Answer

Page No 322:
Question 10:

find Integral of  


Answer

Page No 322:
Question 11:

find Integral of  


Answer

Page No 322:
Question 12:

find Integral of  


Answer

Page No 322:
Question 13:

find Integral of  


Answer

Page No 322:
Question 14:

find Integral of  


Answer

Page No 322:
Question 15:

find Integral of  


Answer

Page No 322:
Question 16:

find Integral of   [Hint: multiply numerator and denominator by xn − 1 and put xn = t]


Answer

Page No 322:
Question 17:

find Integral of   [Hint: Put sin x = t]


Answer

Page No 323:
Question 18:

find Integral of  


Answer

Page No 323:
Question 19:

find Integral of  


Answer

Page No 323:
Question 20:

find Integral of  


Answer

Page No 323:
Question 21:

find Integral of   [Hint: Put ex = t]


Answer

Page No 327:
Question 1:

 find Integral of   x sin x


Answer

Page No 327:
Question 2:

find Integral of  


Answer

Page No 327:
Question 3:

find Integral of  


Answer

Page No 327:
Question 4:

 find Integral of x logx


Answer

Page No 327:
Question 5:

 find Integral of x log 2x


Answer

Page No 327:
Question 6:

 find Integral of x2 log x


Answer

Page No 327:
Question 7:

find Integral of  


Answer

Page No 327:
Question 8:

find Integral of  


Answer

Page No 327:
Question 9:

find Integral of  


Answer

Page No 327:
Question 10:
Find integral of 


Answer

Page No 327:
Question 11:

Find integral of 


Answer

Page No 327:
Question 12:

Find integral of 


Answer

Page No 327:
Question 13:

Find integral of 


Answer

Page No 327:
Question 14:
Find the integral of 


Answer

Page No 327:
Question 15:

find Integral of  


Answer

Page No 328:
Question 16:

find Integral of  


Answer

Page No 328:
Question 17:

find Integral of  


Answer

Page No 328:
Question 18:

find Integral of  


Answer

Page No 328:
Question 19:

find Integral of  


Answer

Page No 328:
Question 20:

find Integral of  


Answer

Page No 328:
Question 21:

find Integral of  


Answer

Page No 328:
Question 22:

find Integral of  


Answer

Page No 330:
Question 1:

find Integral of  

Answer

Page No 330:
Question 2:

find Integral of  


Answer

Page No 330:
Question 3:

find Integral of  


Answer

Page No 330:
Question 4:

find Integral of  


Answer

Page No 330:
Question 5:

find Integral of  


Answer

Page No 330:
Question 6:

find Integral of  


Answer

Page No 330:
Question 7:

find Integral of  


Answer

Page No 330:
Question 8:

find Integral of  


Answer

Page No 330:
Question 9:

find Integral of  


Answer

Page No 334:
Question 1:

find 


Answer

Page No 334:
Question 2:

Find


Answer

Page No 334:
Question 3:

find 


Answer

Page No 334:
Question 4:

find 


Answer

Page No 334:
Question 5:

find 


Answer

Page No 334:
Question 6:

find 


Answer

Page No 338:
Question 1:

find  


Answer

Page No 338:
Question 2:

find  


Answer

Page No 338:
Question 3:

find 


Answer

Page No 338:
Question 4:

find 


Answer

Page No 338:
Question 5:

find 


Answer

Page No 338:
Question 6:

find 


Answer

Page No 338:
Question 7:

find 


Answer

Page No 338:
Question 8:

find 


Answer

Page No 338:
Question 9:

find 


Answer

Page No 338:
Question 10:

find 


Answer

Page No 338:
Question 11:

find 


Answer

Page No 338:
Question 12:

find 


Answer

Page No 338:
Question 13:

find 


Answer

Page No 338:
Question 14:

find 


Answer

Page No 338:
Question 15:

find 


Answer

Page No 338:
Question 16:

find 


Answer

Page No 338:
Question 17:

find 


Answer

Page No 338:
Question 18:

find 


Answer

Page No 338:
Question 19:

find 


Answer

Page No 338:
Question 20:

find 


Answer

Page No 340:
Question 1:

find 


Answer

Page No 340:
Question 2:

find 


Answer

Page No 340:
Question 3:

find 


Answer

Page No 340:
Question 4:

find 


Answer

Page No 340:
Question 5:

find 


Answer

Page No 340:
Question 6:

find 


Answer

Page No 340:
Question 7:

find 


Answer

Page No 340:
Question 8:

find 


Answer

Page No 347:
Question 1:

find 


Answer

Page No 347:
Question 2:

find 


Answer

Page No 347:
Question 3:

find 


Answer

Page No 347:
Question 4:

find 


Answer

Page No 347:
Question 5:

find 


Answer

Page No 347:
Question 6:

find 


Answer

Page No 347:
Question 7:

find 


Answer

Page No 347:
Question 8:

find 


Answer

Page No 347:
Question 9:

find 


Answer

Page No 347:
Question 10:

find 


Answer

Page No 347:
Question 11:

find 


Answer

Page No 347:
Question 12:

find 


Answer

Page No 347:
Question 13:

find 


Answer

Page No 347:
Question 14:

find 


Answer

Page No 347:
Question 15:

find 


Answer

Page No 347:
Question 16:

find 


Answer

Page No 347:
Question 17:

find 


Answer

Page No 347:
Question 18:

find 


Answer

Page No 347:
Question 19:

Show that if f and g are defined as and 


Answer

Page No 352:
Question 1:

find Integral of  


Answer

Page No 352:
Question 2:

find Integral of  


Answer

Page No 352:
Question 3:

find Integral of   [Hint: Put]


Answer

Page No 352:
Question 4:

find Integral of  


Answer

Page No 352:
Question 5:

find Integral of   


Answer

Page No 352:
Question 6:

find Integral of  


Answer

Page No 352:
Question 7:

find Integral of  


Answer

Page No 352:
Question 8:

find Integral of  


Answer

Page No 352:
Question 9:

find Integral of  


Answer

Page No 352:
Question 10:

find Integral of  


Answer

Page No 352:
Question 11:

Find integral of 


Answer

Page No 352:
Question 12:

Find integral of 


Answer

Page No 352:
Question 13:

find Integral of     


Answer

Page No 352:
Question 14:

find Integral of    


Answer

Page No 352:
Question 15:

 find Integral of  


Answer

Page No 352:
Question 16:

 find Integral of  


Answer

Page No 352:
Question 17:

 find Integral of  


Answer

Page No 352:
Question 18:

 find Integral of  


Answer

Page No 352:
Question 19:

Find the integral of 


Answer

Page No 352:
Question 20:

 find Integral of  


Answer

Page No 352:
Question 21:

 find Integral of  


Answer

Page No 352:
Question 22:

 find Integral of  


Answer

Page No 353:
Question 23:

 find Integral of  


Answer

Page No 353:
Question 24:

find Integral of   


Answer

Page No 353:
Question 25:

find 


Answer

Page No 353:
Question 26:

find 


Answer

Page No 353:
Question 27:

find 


Answer

Page No 353:
Question 28:

find 


Answer

Page No 353:
Question 29:

find 


Answer

Page No 353:
Question 30:

find 


Answer

Page No 353:
Question 31:

find 


Answer

Page No 353:
Question 32:

find 


Answer

Page No 353:
Question 33:

find 


Answer

Page No 353:
Question 34:

prove that 


Answer

Page No 353:
Question 35:

prove that


Answer

Page No 353:
Question 36:

prove that 


Answer

Page No 353:
Question 37:

prove that 


Answer

Page No 353:
Question 38:

prove that


Answer

Page No 353:
Question 39:

prove that


Answer

Page No 299:
Question 21:
The anti derivative of equals



  •  


    • Answer

    Page No 299:
    Question 22:
    If such that f(2) = 0, then f(x) is






    • Answer

    Page No 305:
    Question 38:
    equals


    • Answer

    Page No 305:
    Question 39:
    equals






    • Answer

    Page No 307:
    Question 23:
     is equal to


  • tan x + cot x + C
  • tan x + cosec x + C
  • − tan x + cot x + C
  • tan x + sec x + C

    • Answer

    Page No 307:
    Question 24:
     equals


  • − cot (exx) + C
  • tan (xex) + C
  • tan (ex) + C
  • cot (ex) + C

    • Answer

    Page No 316:
    Question 24:
    equals


  • x tan−1 (x + 1) + C
  • tan− 1 (x + 1) + C
  • (x + 1) tan−1 x + C
  • tan−1 x + C

    • Answer

    Page No 316:
    Question 25:
    equals






    • Answer

    Page No 328:
    Question 23:
     equals






    • Answer

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