Question

Question attached as screenshot belowPlease help me with my calculus homework I am paying close attention

Answer 1

Given:

`\int ^1_(-1)(1)/(x^2+1)dx`

To evaluate:

As we know,

`\int ^{}_{}\frac{1}{x^2+1^{}}dx=\tan ^(-1)(x)+C`

So, we have

`\begin{gathered} \int ^1_(-1)(1)/(x^2+1)dx=\tan ^(-1)(1)-\tan ^(-1)(-1) \\ =(\pi)/(4)-(-(\pi)/(4)) \\ =(\pi)/(4)+(\pi)/(4) \\ =(2\pi)/(4) \\ =(\pi)/(2) \end{gathered}`

Hence, the answer is,

`(\pi)/(2)`