Elective Mathematics

1If the velocity is v = 6t, the displacement from t = 0 to t = 2 is

2Find the volume generated when y = x² from x = 0 to x = 1 is rotated about the x-axis.

3The area between y = x³ and the x-axis from x = −1 to x = 1 is

4The area between y = 4 − x² and the x-axis is

5The area under y = x² from x = 0 to x = 3 is

6The volume generated when y = x from 0 to 3 is rotated about the x-axis is

7The area under y = 2x from x = 1 to x = 4 is

8The volume formed when the region under y = f(x) from a to b is rotated about the x-axis is

9Find the area under y = x² from x = 0 to x = 3.

10A particle starts at the origin with velocity v = 2t m/s. How far does it travel in the first 3 s?