Question

Who helps me with these integral calculus exercises?

Answer 1

`\int_(0)^(1)(1)/(1+x^2)dx`

The integral above is definite so we must first calculate for indefinite one.


`\int{(1)/(1+x^2)dx}`

Rule:
`\int{(1)/(a^2+b^2)dx}=(1)/(b)*\arctan((a)/(b))`.

Now we apply this rule and get:


`\int{(1)/(1+x^2)}=(1)/(1)*\arctan((x)/(1))`

Or just simply:
`\arctan(x)`

Now we integrate:


`\arctan(x)\Big\vert_(0)^(1)`


`\arctan(1)-\arctan(0)`


`(\pi)/(4)-0\implies\boxed{(\pi)/(4)}`