JEE Mains · Maths · STD 12 - 8. Application and integration
If the area of the region \(\{(x, y):|x-5| \leq y \leq 4 \sqrt{x}\}\) is A , then 3 A is equal to _____ .
- A 368
- B 367
- C 366
- D 365
Answer & Solution
Correct Answer
(A) 368
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & A=\int_1^{25} 4 \sqrt{x} d x-\frac{1}{2} \times 4 \times 4-\frac{1}{2} \times 20 \times 20 \\ & A=\left[\frac{4 x^{3 / 2}}{\frac{3}{2}}\right]^{25}-8-200 \\ & A=\frac{8}{3}(125-1)-208 \\ & A=\frac{368}{3} \Rightarrow 3 A=368\end{aligned}\)
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