JEE Mains · Maths · STD 12 - 8. Application and integration
The area of the region \(R=\{(x,y):xy\le8, 1\le y\le x^{2}, x\ge0\}\) is
- A \(\frac{1}{3}(49~log_{e}(2)-15)\)
- B \(\frac{2}{3}(20~log_{e}(2)+9)\)
- C \(\frac{2}{3}(24~log_{e}(2)-7)\)
- D \(\frac{1}{3}(40~log_{e}(2)+27)\)
Answer & Solution
Correct Answer
(C) \(\frac{2}{3}(24~log_{e}(2)-7)\)
Step-by-step Solution
Detailed explanation
\(A=\int_{1}^{2}(x^{2}-1)dx+\int_{2}^{8}(\frac{8}{x}-1)dx\) \(A=8~log_{e}4-\frac{14}{3}=16~log_{e}2-\frac{14}{3}\) \(=\frac{2}{3}(24~log_{e}2-7)\)
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