AP EAMCET · Maths · Definite Integration
\(\int_{-5 \pi}^{5 \pi}(1-\cos 2 x)^{\frac{5}{2}} d x=\)
- A \(\frac{64 \sqrt{2}}{5}\)
- B \(\frac{128 \sqrt{2}}{5}\)
- C \(\frac{256 \sqrt{2}}{3}\)
- D \(\frac{128 \sqrt{2}}{3}\)
Answer & Solution
Correct Answer
(D) \(\frac{128 \sqrt{2}}{3}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} \quad \mathrm{I} & =\int_{-5 \pi}^{5 \pi}(1-\cos 2 x)^{\frac{5}{2}} d x=2 \int_0^{5 \pi}\left(2 \sin ^2 x\right)^{\frac{5}{2}} d x \\ \Rightarrow \mathrm{I} & =(2)^3 \sqrt{2} \int_0^{5 \pi} \sin ^5 x d x \end{aligned}\) Let…
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