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CBSE CLASS XII

Application of Integrals

Q. 1. Find the area of the region in the first quadrant enclosed by the x-axis, the line y = x and the circle

Q. 2. Find the area of the region bounded by the ellipse.

Q. 3. Find the area of the region bounded by the parabola y = x² and y = .

Q. 4. Find the area of the smaller part of the circle x² + y² = a² cut off by the linex=.

Q. 5. Using integration, find the area of the region bounded by the triangle whose vertices are (1, 0), (2,2) and (3, 1).

Q. 6. Prove that the curves y² = 4x and x² = 4y divide the area of the square bounded by x=0, x=4, y=4 and y=0 into three equal parts.

Q. 7. Sketch the graph of y=

Q. 8. Using the method of integration, find the area bounded by the curve .

Q. 9. Find the area of the smaller region bounded by the ellipse .

Q. 10. Using integration, find the area of the triangular region, the equations of whose sides are y=2x + 1, y=3x +1 and  x = 4.

Q. 11. Find the area of the region

Q. 12. Find the area of the region between the circles x2 + y2 = 4 and (x – 2)2 + y2 = 4.

Q. 13. Find the area bounded by the ellipse and the co-ordinates x = ae and x = 0where b2=a2(1 – e2) and e<1.

Q. 14. Find the area bounded by the curve y² = 4a²(x – 1) and the lines x = 1and y = 4a.

Q. 15. Using integration, find the area of the region bounded by the following curves, after making a rough sketch:
y = 1 +
Q. 16. Draw a rough sketch of the curves y = sinx and y = cosx as x varies from o to and find the area of the region enclosed by them and x-axis.

Prepared By Anil Kumar Tondak
M.Sc.(Maths), M.Ed.,
M.A.(Eco),M.B.A.(Mkt)
Mob No. 9811363962