WBJEE · Maths · Area Under Curves
The area of the region, bounded by the curves \(y=\sin ^{-1} x+x(1-x)\) and
\(y=\sin ^{-1} x-x(1-x)\) in the first quadrant, is
- A 1
- B \(\frac{1}{2}\)
- C \(\frac{1}{3}\)
- D \(\frac{1}{4}\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{3}\)
Step-by-step Solution
Detailed explanation
\(\sin ^{-1} x\) is defined, if \(-1 \leq x \leq 1\) In first quadrant \(0 \leq x \leq 1\) and \(x(1-x) \geq 0\) \(\therefore\) \(y=\sin ^{-1} x+x(1-x)\) Lies above \(y=\sin ^{-1} x-x(1-x)\) On solving, we get \(2 x(1-x)=0\)…
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