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. 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:
Prepared By Anil Kumar Tondak