# Find the area of the region given the boundaries

1. Apr 3, 2017

### beefiestcrib55

1. The problem statement, all variables and given/known data
The curve of y= 4/(x^2+4), the x-axis, and the vertical lines x = -2 and x = 2

2. Relevant equations

3. The attempt at a solution

2. Apr 4, 2017

### Math_QED

Hello beefiestcrib55!

To begin, every member here will appreciate if you type out your work. Most members won't even bother if you post images.

There are a couple of things wrong about your approach. You set up the integral correctly, but then a couple of things went wrong:

2) You need to perform a substitution, you cannot (without experience) evaluate the integral into a primitive function in one step!
3)$\int \frac{1}{x^2 + 1} dx = \arctan(x) + c$, not $\arctan(x^2)+c$
4) Although your bounds should be changed by the substitution, why would you fill in $1$ as upperbound if you have $2$ as upperbound?

3. Apr 4, 2017

### Eclair_de_XII

Specifically, $\int \frac{dx}{x^2+a^2}=\frac{1}{a}tan^{-1}(\frac{x}{a})$ or in his case, $\int \frac{dx}{\frac{x^2}{a^2}+1}=\frac{1}{a}tan^{-1}(\frac{x}{a})$. Also, $tan^{-1}(0)≠\frac{\pi}{2}$. For future reference, $\lim_{x \rightarrow \infty} {tan^{-1}(x)}=\frac{\pi}{2}$, and $\lim_{x \rightarrow -\infty} {tan^{-1}(x)}=-\frac{\pi}{2}$.

Last edited: Apr 4, 2017