Question

Hi there, I am having trouble solving these two integrals as I continue to get the answers wrong:

Answer 1

663.84 degrees

Explanations:

Given the integral function

`\int_(-\infty)^8(8)/(x^2+4)dx`

Since 8 is a constant, it will be outside the integral function to have:

`\begin{gathered} 8\int_(-\infty)^8(1)/(x^2+4)dx \\ 8\int_(-\infty)^8(1)/(x^2+2^2)dx \end{gathered}`

Using the general rule shown below;

`\int(1)/(x^2+a^2)dx=(1)/(a)tan^(-1)((x)/(a))+C`

Comparing with the given integral, a = 2, such that;

`\begin{gathered} 8\int_(-\infty)^8(1)/(x^2+2^2)=[8((1)/(2)tan^(-1)((x)/(2)))]_(-\infty)^8 \\ \int_(-\infty)^8(8)/(x^2+2^2)=[4tan^(-1)((x)/(2))]_(-\infty)^8 \end{gathered}`

Substitute the limits

`\begin{gathered} \int_(-\infty)^8(8)/(x^2+2^2)=[4tan^(-1)((8)/(2))-4tan^(-1)(-(\infty)/(2))] \\ \int_(-\infty)^8(8)/(x^2+2^2)=[4(75.96)-4(-90)] \\ \int_(-\infty)^8(8)/(x^2+2^2)=303.84+360=663.84^0 \\ \end{gathered}`