AP EAMCET · Maths · Definite Integration
If \(\int^4 x \sqrt{x^2-1} d x=\alpha(k)^\beta\), then \(\alpha \beta\) is equal to
- A \(\frac{9}{2}\)
- B \(\frac{1}{2}\)
- C \(\frac{1}{3}\)
- D \(\frac{3}{2}\)
Answer & Solution
Correct Answer
(B) \(\frac{1}{2}\)
Step-by-step Solution
Detailed explanation
\(\int_1^4 x \sqrt{x^2-1} d x=\alpha(k)^\beta\) Let \(I=\int_1^4 x \sqrt{x^2-1} d x\) Let \(x^2-1=t\) \(\Rightarrow x d x=\frac{d t}{2}\) Upper limit \(=t=4^2-1=15\) Lower limit \(=t=1^2-1=0\)…
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