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JEE Main · 2024 · 30 Jan 2024 · Shift 1 · Area Under Curves

The area (in square units) of the region bounded by the parabola

y^{2} = 4 (x - 2)

and the line

y = 2 x - 8

(A)8
(B)9✓ Correct
(C)6
(D)7

Answer: (B)

Solution

With

X = x - 2

, the parabola is

y^{2} = 4 X

and the line becomes

y = 2 X - 4

.

Substituting

X = \frac{y + 4}{2}

:

y^{2} = 2 (y + 4) \Rightarrow y^{2} - 2 y - 8 = 0 \Rightarrow y = - 2, 4

.

A = \int_{- 2}^{4} (\frac{y + 4}{2} - \frac{y ^{2}}{4}) d y = [\frac{y ^{2}}{4} + 2 y - \frac{y ^{3}}{12}]_{- 2}^{4} = 9

JEE Main · 2024 · 30 Jan 2024 · Shift 1 · Single correct option

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