Evaluate $\int _ { - 1 } ^ { 4 } \left| 9 - x ^ { 2 } \right| d x$
A) 20
B) 15
C) 12
D) 30

Name: Evaluate $\int _ { - 1 } ^ { 4 } \left| 9 - x ^ { 2 } \right| d x$ A) 20 B) 15 C) 12 D) 30
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Question

Quizplus · Accepted Answer

The function $9 - x^2$ is positive between $x = -3$ and $x = 3$, and negative outside this interval. The integral can be split into three parts: $\int_{-1}^{3} (9 - x^2) dx$ and $\int_{3}^{4} (x^2 - 9) dx$. Calculating these integrals and summing their absolute values gives 30.

Evaluate ∫−14∣9−x2∣dx\int _ { - 1 } ^ { 4 } \left| 9 - x ^ { 2 } \right| d x∫−14​​9−x2​dx

Evaluate $\int _ { - 1 } ^ { 4 } \left| 9 - x ^ { 2 } \right| d x$