∫x^(3)+x dx from [−2,0 ]

[mama]

How can I evaluate the definite integral ∫x^(3)+x dx from [−2,0 ]?

 

[MarkFL]

Hello, and welcome to FMH!

I would utilize the fact that the integrand is an odd function and write:

[MATH]I=-\int_0^2 x^3+x\,dx[/MATH]
To find the anti-derivative, use the power rule for integration on each term:

[MATH]\int_a^b x^n\,dx=\left.\frac{x^{n+1}}{n+1}\right|_a^b[/MATH]
Can you proceed?

 

[mama]

Thanks, I didn't remind the fact, that i need to use the fundamental theorem of calc