JEE Mains · Maths · STD 12 - 7.2 definite integral
If the integral \(525 \int_0^{\frac{\pi}{2}} \sin 2 x \cos ^{\frac{11}{2}} x\left(1+\cos ^{\frac{5}{2}} x\right)^{\frac{1}{2}} d x\) is equal to \((n \sqrt{2}-64)\), then \(n\) is equal to
- A \(176\)
- B \(175\)
- C \(170\)
- D \(174\)
Answer & Solution
Correct Answer
(A) \(176\)
Step-by-step Solution
Detailed explanation
\(I=\int_0^{\frac{\pi}{2}} \sin 2 x \cdot(\cos x)^{\frac{11}{2}}\left(1+(\cos x)^{\frac{5}{2}}\right)^{\frac{1}{2}} d x\) Put \(\cos x=t^2 \Rightarrow \sin x d x=-2 t d t\)…
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