Question

Find the area between the curve and the x-axis over the indicated interval y = 36-x?. [-6, 6] The area under the curve is (Simplify your answer.)

Answer 1

we know that

To find out the area between the curve and the x-axis over the indicated interval, we need to calculate the integral of the function over the indicated interval.

so

`\int (36-x^2)dx=(36x-(x^3)/(3))`

Eavaluate over the indicated interval

`\begin{gathered} (36\cdot6-(6^3)/(3))-(36\cdot(-6)-(-6^3)/(3)) \\ 144-(-216+72) \\ 288 \end{gathered}`

the area is 288 units squares