AP EAMCET · Maths · Definite Integration
\(\int_{-2}^2\left(4-x^2\right)^{\frac{5}{2}} d x=\)
- A \(40 \pi\)
- B \(20 \pi\)
- C \(\frac{5 \pi}{32}\)
- D \(\frac{5 \pi}{32}\)
Answer & Solution
Correct Answer
(B) \(20 \pi\)
Step-by-step Solution
Detailed explanation
\(I=\int_{-2}^2\left(4-x^2\right)^{5 / 2} d x=2 \int_0^2\left(4-x^2\right)^{\frac{5}{2}} d x\) Let \(x=2 \sin \theta \Rightarrow d x=2 \cos \theta d \theta\)…
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