## nickhouraney integrate (x^3+x^4tanx) dx from x=-pi/4 to pi/4 10 months ago 10 months ago

1. nickhouraney

$\int\limits_{-\pi/4}^{\pi/4} (x^3+x^4tanx) dx$

2. hartnn

check whether x^3+x^4 tan x is odd function or not. if its an odd function, then the integral =0

3. hartnn

the function is odd if f(x) = -f(-x) and a property of indefinite integral is $$\int \limits_{-a}^af(x)dx=0$$ if f(x) is odd function, $$\int \limits_{-a}^af(x)dx=2\int \limits_{0}^af(x)dx$$ if f(x) is even function.

4. nickhouraney

what if its neither lol

5. hartnn

if its neither, you have to integrate the function as it is....no simplification...