AP EAMCET · Maths · Indefinite Integration
If \(\int f(x) d x=\psi(x)\), then \(\int x^5 f\left(x^3\right) d x=\)
- A \(\frac{1}{3}\left[x^3 \psi\left(x^3\right)\right]-\int x^2 \psi\left(x^3\right) d x\)
- B \(\frac{1}{3}\left[x^3 \psi\left(x^3\right)\right]+\int x^2 \psi\left(x^3\right) d x\)
- C \(-\frac{1}{3}\left[x^3 \psi\left(x^3\right)\right]-\int x^3 \psi\left(x^3\right) d x\)
- D \(-\frac{1}{3}\left[x^3 \psi\left(x^3\right)\right]+\int x^3 \psi\left(x^3\right) d x\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{3}\left[x^3 \psi\left(x^3\right)\right]-\int x^2 \psi\left(x^3\right) d x\)
Step-by-step Solution
Detailed explanation
\(\int f(\mathrm{x}) \mathrm{dx}=\psi(\mathrm{x})\) Let \(\mathrm{I}=\int x^5 f\left(x^3\right) d x=\int x^3 f\left(x^3\right) x^2 d x\) Let \(x^3=t \Rightarrow 3 x^2 d x=d t \Rightarrow x^2 d x=\frac{d t}{3}\)…
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