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JEE Main 20245 AprilMorning Shift
Exam
JEE Main
Year
2024
Date
5 April
Shift
Morning Shift
Subject
Mathematics
Chapter
Area Under Curves

JEE Main 2024 · 5 April · Morning Shift · Mathematics · Area Under Curves

The area of the region enclosed by the parabolas y=x^2-5 x and y=7...

The area of the region enclosed by the parabolas y=x2−5xy=x^2-5 x and y=7x−x2y=7 x-x^2 is

Correct answer

72

Step-by-step solution

y=x^2-5 x and y=7x−x2y=7 x-x^2∫06(g(x)−f(x))dx∫06((7x−x2)−(x2−5x))dx∫06(12x−2x2)dx=[12x22−2x33]06⇒6(6)2−23(6)3=216−144=72 unit 2\begin{aligned} & \int_0^6(g(x)-f(x)) d x \\ & \int_0^6\left(\left(7 x-x^2\right)-\left(x^2-5 x\right)\right) d x \\ & \int_0^6\left(12 x-2 x^2\right) d x=\left[12 \frac{x^2}{2}-\frac{2 x^3}{3}\right]_0^6 \\ & \Rightarrow 6(6)^2-\frac{2}{3}(6)^3 \\ & =216-144=72 \text{ unit }^2 \\ & \end{aligned}$$
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