JEE Mains · Maths · STD 12 - 7.2 definite integral
Let \(\alpha > 0\). If \(\int \limits _0^\alpha \frac{ x }{\sqrt{ x +\alpha}-\sqrt{ x }} dx =\frac{16+20 \sqrt{2}}{15}\), then \(\alpha\) is equal to :
- A \(2\)
- B \(4\)
- C \(\sqrt{2}\)
- D \(2 \sqrt{2}\)
Answer & Solution
Correct Answer
(A) \(2\)
Step-by-step Solution
Detailed explanation
After rationalising \(\int \limits_0^\alpha \frac{ x }{\alpha}(\sqrt{ x +\alpha}+\sqrt{ x })\) \(\int \limits _0^\alpha \frac{1}{\alpha}\left[( x +\alpha)^{3 / 2}-\alpha( x +\alpha)^{1 / 2}+ x ^{3 / 2}\right]\)…
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