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JEE Main 20257 AprilMorning Shift
Exam
JEE Main
Year
2025
Date
7 April
Shift
Morning Shift
Subject
Mathematics
Chapter
Area Under Curves

JEE Main 2025 · 7 April · Morning Shift · Mathematics · Area Under Curves

If the area of the region bounded by the curves (y=4- (x^2)/(4) )...

If the area of the region bounded by the curves (y=4-x24\frac{x^2}{4}) and (y=x−42\frac{x-4}{2}) is equal to (α\alpha), then (6 α\alpha) equals

Options

  1. A250
  2. B210
  3. C240
  4. D220

Correct answer

A. 250

Step-by-step solution

 Area =∫−64{(4−x24)−(x−42)}dx=∫−64{−x24−x−62}dxα=−x312−x24+6x∣−64=1253∴6α=250\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} \\ & \therefore 6 \alpha=250\end{aligned}
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