JEE Mains · Maths · STD 12 - 8. Application and integration
The area of the region enclosed between the parabolas \(y ^{2}=2 x -1\) and \(y ^{2}=4 x -3\) is
- A 0.33
- B 0.17
- C 0.67
- D 0.75
Answer & Solution
Correct Answer
(A) 0.33
Step-by-step Solution
Detailed explanation
Required area \(=2 \int \limits_{0}^{1}\left(\frac{y^{2}+3}{4}-\frac{y^{2}+1}{2}\right) d y\) \(=2 \int \limits_{0}^{1} \frac{1-y^{2}}{4} d y=\frac{1}{2}\left|y-\frac{y^{3}}{3}\right|_{0}^{1}=\frac{1}{3}\)
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