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

$\int (36-x^2)dx=(36x-\frac{x^3}{3})$

Eavaluate over the indicated interval

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

the area is 288 units squares