Use the limit process to find the area of the region between the graph of the function $y = 16 - x ^ { 2 }$ and $x$-axis over the interval $[ - 4,4 ]$
A) $\frac { 704 } { 3 }$
B) $\frac { 256 } { 3 }$
C) $\frac { 760 } { 3 }$
D) $\frac { 352 } { 3 }$
E) $\frac { 128 } { 3 }$

Question

Quizplus · Accepted Answer

The area under the curve $y = 16 - x^2$ from $[-4, 4]$ can be found using the integral $\int_{-4}^{4} (16 - x^2) dx$. Solving this integral gives $\left[16x - \frac{x^3}{3}\right]_{-4}^{4}$ which simplifies to $\left(64 - \frac{64}{3}\right) - \left(-64 + \frac{64}{3}\right) = 128 - \frac{128}{3} = \frac{256}{3}$.

Use the Limit Process to Find the Area of the Region