Question

What is the antiderivative of `2sin(t/2)`?

Answer 1

Anti-derivative is indefinite integral of a function.

Explanation:

In other words an anti-derivative is a function that reverses what derivative does.
Therefore to find the anti-derivative we need to find a function `f(t)` such that

`f'(t)=2sin(t/2)`
Integrating both sides with respect to `t` we get

`intf'(t)dt=int2sin(t/2)dt`
`=>f(t)=int2sin(t/2)dt`

Integrating RHS we get
`f(t)=2(-cos(t/2))/(1/2)+C`
where `C` is a constant of integration
`=>f(t)=-4cos(t/2)+C`