Q.1 . Evaluate the following indefinite integrals:
Q.2. Using the method of integration by parts evaluate the following integral:
Q.3. Evaluate the following integrals:
Q. 4. Evaluate the following integrals:
Q.5. First find the partial fraction composition and then evaluate the following integral:
Q. 6. Find the area of the shaded region by (i) integrating with respect to x and (ii) integrating with respect to y. [10]
Q.7 (i) Sketch the region enclosed by the following curves.
(ii) Find the volume of the solid that results when the region enclosed by the following curves is revolved around the x-axis.
Q.8 Use cylindrical shells method to find the volume of the solid generated when the region enclosed by the following curves is revolved about the y-axis. First sketch the region.
Q.9 Sketch the curve and then find the exact arc length of the following curve
y = x2/3
over the interval x = 0 to x = 8.
Q. 10. Derive the following identity:
