If the area bounded by the curves x 2 + y ≤ 2 and y ≥ x is k 2 sq. units, then 2 k is equal to

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Question: Answered & Verified by Expert

If the area bounded by the curves

x^{2} + y \leq 2

and

y \geq x

is

\frac{k}{2}

sq. units, then

2 k

is equal to

MathematicsArea Under CurvesJEE Main

Options:

A $9$
B $27$
C $18$
D $32$

Solution:

2201 Upvotes Verified Answer

The correct answer is:

18

Required area is

A = \int_{- 2}^{1} ((2 - x^{2}) - x) d x

= {[2 x - \frac{x^{3}}{3} - \frac{x^{2}}{2}]}_{- 2}^{1}

= {[2 x - \frac{x^{3}}{3} - \frac{x^{2}}{2}]}_{- 2}^{1}

= 6 - \frac{9}{3} + \frac{3}{2} = \frac{9}{2}

sq. units

∴ 2 k = 18

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