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JEE Main · 2024 · 05 Apr 2024 · Shift 1 · Area Under Curves

The area of the region enclosed by the parabolas

y = x^{2} - 5 x

and

y = 7 x - x^{2}

is ____.

Answer: 72

Solution

The parabolas

y = x^{2} - 5 x

and

y = 7 x - x^{2}

meet where

x^{2} - 5 x = 7 x - x^{2} \Rightarrow 2 x^{2} - 12 x = 0 \Rightarrow x = 0, 6

. On

[0, 6]

the upper curve is

y = 7 x - x^{2}

:

Area = \int_{0}^{6} [(7 x - x^{2}) - (x^{2} - 5 x)] d x = \int_{0}^{6} (12 x - 2 x^{2}) d x = [6 x^{2} - \frac{2}{3} x^{3}]_{0}^{6} = 216 - 144 = 72.

Re-derivation gives

72

, matching the stored key and Allen.

JEE Main · 2024 · 05 Apr 2024 · Shift 1 · Integer answer

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