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Class 12
Maths :-NCERT Solutions - Application Of Integrals

Page No 366:
Question 4:

Find the area of the region bounded by the ellipse 


Page No 366:
Question 5:

Find the area of the region bounded by the ellipse 


Page No 366:
Question 6:

Find the area of the region in the first quadrant enclosed by x-axis, line and the circle 


Page No 366:
Question 7:

Find the area of the smaller part of the circle x2 + y2 = a2 cut off by the line 


Page No 366:
Question 9:

Find the area of the region bounded by the parabola x2 and 


Page No 366:
Question 10:

Find the area bounded by the curve x2 = 4y and the line x = 4– 2


Page No 366:
Question 11:

Find the area of the region bounded by the curve y2 = 4x and the line x = 3


Page No 371:
Question 1:

Find the area of the circle 4x2 + 4y2 = 9 which is interior to the parabola x2 = 4y


Page No 371:
Question 2:

Find the area bounded by curves (x – 1)2 + y2 = 1 and x2 + y 2 = 1


Page No 371:
Question 3:

Find the area of the region bounded by the curves y = x+ 2, xx = 0 and x = 3


Page No 375:
Question 1:

Find the area under the given curves and given lines:

(i) y = x2x = 1, x = 2 and x-axis

(ii) y = x4x = 1, x = 5 and x –axis


Page No 375:
Question 2:

Find the area between the curves y = x and y = x2


Page No 375:
Question 3:

Find the area of the region lying in the first quadrant and bounded by y = 4x2x = 0, y = 1 and = 4


Page No 375:
Question 4:

Sketch the graph of and evaluate


Page No 375:
Question 5:

Find the area bounded by the curve y = sin between x = 0 and x = 2π


Page No 375:
Question 6:

Find the area enclosed between the parabola y2 = 4ax and the line y mx


Page No 375:
Question 7:

Find the area enclosed by the parabola 4y = 3x2 and the line 2y = 3x + 12


Page No 375:
Question 8:

Find the area of the smaller region bounded by the ellipse and the line 


Page No 375:
Question 9:

Find the area of the smaller region bounded by the ellipse  and the line 


Page No 375:
Question 10:

Find the area of the region enclosed by the parabola x2 = y, the line y = x + 2 and x-axis


Page No 375:
Question 11:

Using the method of integration find the area bounded by the curve 

[Hint: the required region is bounded by lines x + y = 1, x – y = 1, – x + y = 1 and – x – = 11]


Page No 376:
Question 12:

Find the area bounded by curves 


Page No 376:
Question 13:

Using the method of integration find the area of the triangle ABC, coordinates of whose vertices are A (2, 0), B (4, 5) and C (6, 3)


Page No 376:
Question 14:

Using the method of integration find the area of the region bounded by lines:

2x + y = 4, 3x – 2y = 6 and x – 3+ 5 = 0


Page No 376:
Question 15:

Find the area of the region 


Page No 366:
Question 12:
Area lying in the first quadrant and bounded by the circle x2 + y2 = 4 and the lines x = 0 and = 2 is


  • π



  • Page No 366:
    Question 13:
    Area of the region bounded by the curve y2 = 4xy-axis and the line y = 3 is


  • 2



  • Page No 372:
    Question 6:
    Smaller area enclosed by the circle x2 + y2 = 4 and the line x + y = 2 is


  • 2 (π – 2)
  • π – 2
  • 2π – 1
  • 2 (π + 2)
  • Page No 372:
    Question 7:
    Area lying between the curve y2 = 4x and y = 2x is






  • Page No 376:
    Question 16:
    Area bounded by the curve y = x3, the x-axis and the ordinates x = –2 and x = 1 is


  •  – 9



  • Page No 376:
    Question 17:
    The area bounded by the curvex-axis and the ordinates x = –1 and x = 1 is given by
    [Hint: y = x2 if x > 0 and y = –x2 if x < 0]


  • 0



  • Page No 376:
    Question 18:
    The area of the circle x2 + y2 = 16 exterior to the parabola y2 = 6x is






  • Page No 376:
    Question 19:
    The area bounded by the y-axis, y = cos x and y = sin x when