The area bounded by $y = x ^ { 2 } - 9$ and $y = 9 - x ^ { 2 }$ is

A)72
B)68
C)64
D)60
E)56

Name: The area bounded by $y = x ^ { 2 } - 9$ and $y = 9 - x ^ { 2 }$ is A)72 B)68 C)64 D)60 E)56
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Question

The area bounded by $y = x ^ { 2 } - 9$ and $y = 9 - x ^ { 2 }$ is

A)72
B)68
C)64
D)60
E)56

Quizplus · Accepted Answer

The curves intersect at $x = -3$ and $x = 3$. The area between the curves is calculated by integrating the difference of the functions from $-3$ to $3$: $\int_{-3}^{3} [(9 - x^2) - (x^2 - 9)] \, dx = \int_{-3}^{3} (18 - 2x^2) \, dx$. Evaluating this integral gives an area of 72.

The Area Bounded By y=x2−9y = x ^ { 2 } - 9y=x2−9

The Area Bounded By $y = x ^ { 2 } - 9$