JEE Mains · Maths · STD 12 - 8. Application and integration
The area bounded by the curve \(y=\left|x^{2}-9\right|\) and the line \(y=3\) is
- A \(4(2 \sqrt{3}+\sqrt{6}-4)\)
- B \(4(4 \sqrt{3}+\sqrt{6}-4)\)
- C \(8(4 \sqrt{3}+2 \sqrt{6}-9)\)
- D \(8(4 \sqrt{3}+\sqrt{6}-9)\)
Answer & Solution
Correct Answer
(C) \(8(4 \sqrt{3}+2 \sqrt{6}-9)\)
Step-by-step Solution
Detailed explanation
Area of shaded region \(=2 \int_{0}^{3}(\sqrt{9+y}-\sqrt{9-y}) d y+2 \int_{3}^{9}(\sqrt{9-y}) d y\) \(=2\left[\int_{0}^{3}(9+y)^{1 / 2} d y-\int_{0}^{3}(9-y)^{1 / 2} d y+\int_{3}^{9}(9-y)^{1 / 2} d y\right]\)…
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