AP EAMCET · Maths · Definite Integration
\(\int_1^3 x^n \sqrt{x^2-1} d x=6\), then \(n=\)
- A \(2\)
- B \(3\)
- C \(4\)
- D \(5\)
Answer & Solution
Correct Answer
(B) \(3\)
Step-by-step Solution
Detailed explanation
Let \(I=\int_1^3 x \sqrt[n]{x^2-1} d x=6\) \(=\frac{1}{2} \int_1^3 2 x\left(x^2-1\right)^{\frac{1}{n}} d x=6\) \(\Rightarrow\left[\frac{\left(n^2-1\right)^{\frac{1}{n}+1}}{\frac{1}{n}+1}\right]_1^3=12\) \(\Rightarrow \quad \frac{(8)^{\frac{1}{n}+1}}{\frac{1}{n}+1}=12\)…
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