JEE Mains · Maths · STD 12 - 7.2 definite integral
If the value of the integral \(\int \limits_{0}^{\frac{1}{2}} \frac{x^{2}}{\left(1-x^{2}\right)^{3 / 2}} d x\) is \(\frac{ k }{6},\) then \(k\) is equal to
- A \(2 \sqrt{3}-\pi\)
- B \(3 \sqrt{2}+\pi\)
- C \(3 \sqrt{2}-\pi\)
- D \(2 \sqrt{3}+\pi\)
Answer & Solution
Correct Answer
(A) \(2 \sqrt{3}-\pi\)
Step-by-step Solution
Detailed explanation
\(\int_{0}^{1 / 2} \frac{\left(\left( x ^{2}-1\right)+1\right)}{\left(1- x ^{2}\right)^{3 / 2}} d x\) \(\int_{0}^{1 / 2} \frac{ dx }{\left(1- x ^{2}\right)^{3 / 2}}-\int_{0}^{1 / 2} \frac{ dx }{\sqrt{1- x ^{2}}}\)…
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