JEE Mains · Maths · STD 12 - 8. Application and integration
The area of the region \(\left\{(x, y):|x-1| \leq y \leq \sqrt{5-x^{2}}\right\}\) is equal to.
- A \(\frac{5}{2} \sin ^{-1}\left(\frac{3}{5}\right)-\frac{1}{2}\)
- B \(\frac{5 \pi}{4}-\frac{3}{2}\)
- C \(\frac{3 \pi}{4}+\frac{3}{2}\)
- D \(\frac{5 \pi}{4}-\frac{1}{2}\)
Answer & Solution
Correct Answer
(D) \(\frac{5 \pi}{4}-\frac{1}{2}\)
Step-by-step Solution
Detailed explanation
\(| x -1|< y <\sqrt{5- x ^{2}}\) \(\text { When }| x -1|=\sqrt{5- x ^{2}}\) \(( x -1)^{2}=5- x ^{2}\) \(x ^{2}- x -2=0\) \(x =2,-1\) Required Area \(=\) Area of \(\triangle ABC +\) Area of region \(BCD\)…
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