Question

Evaluate the integral by interpreting it in terms of areas.
S^0 on the bottom -6 (5+root36-x^2)dx
I have no idea how to work this problem out, please help!

Answer 1

Take a good look at the integrand, does it look familiar to you ?

Answer 2

the -6 is on the bottom of the integral, um no not really

Answer 3

like this ?\[\large \int\limits_{-6}^0 \color{blue}{5+\sqrt{36-x^2}}\, dx\]

Answer 4

yes

Answer 5

May be rearrange the integrand a bit
\[\large y=\color{blue}{5+\sqrt{36-x^2}}\]

\[\large (y\color{blue}{-5})^2=(\color{blue}{\sqrt{36-x^2}})^2\]

\[\large \color{blue}{x^2}+(y\color{blue}{-5})^2=\color{blue}{36}\]

what about now ? seen this before ?

Answer 6

it has to do with circles right?