JEE Mains · Maths · STD 12 - 8. Application and integration
The area (in sq. units) of the region enclosed by the curves \(y=x^{2}-1\) and \(y=1-x^{2}\) is equal to
- A \(\frac{4}{3}\)
- B \(\frac{8}{3}\)
- C \(\frac{16}{3}\)
- D \(\frac{7}{2}\)
Answer & Solution
Correct Answer
(B) \(\frac{8}{3}\)
Step-by-step Solution
Detailed explanation
\(y=x^{2}-1\) and \(y=1-x^{2}\) \(A=\int_{-1}^{1}\left(\left(1-x^{2}\right)-\left(x^{2}-1\right)\right) d x\) \(A=\int_{-1}^{1}\left(2-2 x^{2}\right) d x=4 \int_{0}^{1}\left(1-x^{2}\right) d x\) \(A=4\left(x-\frac{x^{3}}{3}\right)_{0}^{1}=4\left(\frac{2}{3}\right)=\frac{8}{3}\)
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