TS EAMCET · Maths · Definite Integration
If \(I_n=\int_0^a \frac{x^n}{\sqrt{a^2-x^2}} d x\), then \(\frac{I_8}{I_4}=\)
- A \(\frac{48}{35 a^2}\)
- B \(\frac{35}{48} a^4\)
- C \(\frac{19}{72} a^6\)
- D \(\frac{29}{56} a^4\)
Answer & Solution
Correct Answer
(B) \(\frac{35}{48} a^4\)
Step-by-step Solution
Detailed explanation
We have, \(I_n=\int_0^a \frac{x^n}{\sqrt{a^2-x^2}} d x\) Put, \(x=a \sin \theta \Rightarrow d x=a \cos \theta d \theta\) When \(x=0 \Rightarrow \theta=0\) and \(x=a \Rightarrow \theta=\frac{\pi}{2}\)…
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