Question

How do you find the definite integral of `(x^3+x^4(tanx))dx` from `[-pi/4, pi/4]`?

Answer 1

`0`

Explanation:

It is the integral of an odd function over a symmetric interval.

`f(-x)=-f(x)`

`int_(-a)^af(x)dx=int_(-a)^0f(x)dx+int_0^af(x)dx=`
`=int_a^0-f(-y)dy+int_0^af(x)dx`
`=int_0^af(-y)dy+int_0^af(x)dx`
`=-int_0^af(y)dy+int_0^af(x)dx=0`