Question

How do you evaluate the definite integral `int sintheta d(theta)` from `[0,1]`?

Answer 1

`int_0^1sintheta(d theta)=0.4597`

Explanation:

As `d/(dx)costheta=-sintheta`,

`intsintheta(d theta)=-costheta` and hence

`int_0^1sintheta(d theta)=[-costheta]_0^1`

= `-cos1+cos0` (here `1` in `cos1` represents an angle of `1` radian).

= `-0.5403+1=0.4597`