JEE Mains · Maths · STD 12 - 8. Application and integration
If the area of the region bounded by the curves \(y=4-\frac{x^2}{4}\) and \(y=\frac{x-4}{2}\) is equal to \(\alpha\), then \(6 \alpha\) equals
- A 250
- B 210
- C 240
- D 220
Answer & Solution
Correct Answer
(A) 250
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { Area }=\int_{-6}^4\left\{\left(4-\frac{x^2}{4}\right)-\left(\frac{x-4}{2}\right)\right\} d x \\ & =\int_{-6}^4\left\{-\frac{x^2}{4}-\frac{x-6}{2}\right\} d x \\ & \alpha=-\frac{x^3}{12}-\frac{x^2}{4}+\left.6 x\right|_{-6} ^4=\frac{125}{3} \\ &…
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