TS EAMCET · Maths · Definite Integration
\(\int_3^5(x-3)^3(5-x)^5 d x=\)
- A \(\frac{64}{63}\)
- B \(\frac{25}{7}\)
- C \(\frac{3}{32}\)
- D \(\frac{16}{25}\)
Answer & Solution
Correct Answer
(A) \(\frac{64}{63}\)
Step-by-step Solution
Detailed explanation
\(I=\int_3^5(x-3)^3(5-x)^5 d x\) Let, \(x=3 \cos ^2 \theta+5 \sin ^2 \theta\), so at \(x=3, \theta=0\) and at \(x=5, \theta=\frac{\pi}{2}\) and \(d x=2 \sin 2 \theta d \theta\) Therefore,…
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