# Math Help - Evaluate the definite integrals

1. ## Evaluate the definite integrals

I have absolutely no idea how I'm supposed to do this.

Evaluate each of the following definite integrals:

a) $\int_1^4 \frac{x^2+2x}{\sqrt{x^2}} dx$
b) $\int_{-1}^{1} \frac{1}{v}(3v^3-v^\frac{-1}{3}) dv$

Can anyone point me in the right direction? I've done definite integrals, but none that hard before.

In the region $\displaystyle 1 \leq x \leq 4, \sqrt{x^2} = x$.
So $\displaystyle \int_1^4{\frac{x^2+2x}{\sqrt{x^2}}\,dx} = \int_1^4{\frac{x^2+2x}{x}\,dx} = \int_1^4{x + 2\,dx}$.
Also $\displaystyle \int_{-1}^1{\frac{1}{v}(3v^3 - v^{-\frac{1}{3}})\,dv} = \int_{-1}^1{3v^2 - v^{-\frac{4}{3}}\,dv}$.