# 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.

Thanks in advance

2. Worked out how to do it.

You integrate it first, then multiply it by the bigger number and minus it by the smaller number times the value.

3. The easiest way is to simplify the integrand...

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 $\displaystyle \int_{-1}^1{\frac{1}{v}(3v^3 - v^{-\frac{1}{3}})\,dv} = \int_{-1}^1{3v^2 - v^{-\frac{4}{3}}\,dv}$.