JEE Mains · Maths · STD 12 - 8. Application and integration
The area of the region \(\left\{(x, y): x^2 \leq y \leq 8-x^2, y \leq 7\right\}\) is
- A \(21\)
- B \(18\)
- C \(24\)
- D \(20\)
Answer & Solution
Correct Answer
(D) \(20\)
Step-by-step Solution
Detailed explanation
\(y \geq x^2 \quad y \leq 8-x^2 \quad y \leq 7\) \(x^2=8-x^2\) \(x^2=4\) \(x= \pm 2\) \(2\left(1.7+\int \limits_1^2\left(8-2 x^2\right) d x\right)-2 \int \limits_0^1\left(x^2\right) d x\) \(=2\left[7+\left(8 x-\frac{2 x^3}{3}\right)_1^2\right]-2\left(\frac{x^3}{3}\right)_0^1\)…
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