JEE Mains · Maths · STD 12 - 8. Application and integration
The area (in \(sq. \,units\)) of the region, given by the set \(\left\{(x, y) \in R \times R \mid x \geq 0,2 x^{2} \leq y \leq 4-2 x\right\}\) is:
- A \(\frac{7}{3}\)
- B \(\frac{13}{3}\)
- C \(\frac{17}{3}\)
- D \(\frac{8}{3}\)
Answer & Solution
Correct Answer
(A) \(\frac{7}{3}\)
Step-by-step Solution
Detailed explanation
Required area \(=\int_{0}^{1}\left(4-2 x-2 s^{2}\right) d x=4 x-x^{2}-\left.\frac{2 x^{3}}{3}\right|_{0} ^{1}\) \(=4-1-\frac{2}{3}=\frac{7}{3}\)
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