What is the area bounded by the curves, the lines {x}=0 and {x}=1 ?

Correct Answer is : 232/332 square unit

Correct Answer is : 232/332 square unit

Test Index

UPSC NDA I 2026 Mathematics Paper

Question Numbers: 89-90

For the next two (02) items that follow:

Consider the curves

\mathrm{y}=\mathrm{x}^{2}

and

\mathrm{y}=2|\mathrm{x}|

Question : 90 of 120

Marks: +1, -0

\mathrm{x}=0

\mathrm{x}=1

Solution:

Concept:

Area between the two curves from

x=0

x=1

Explanation:

For

0 \le x \le 1

, we have

|x| = x

So the curves are

y = x^2

and

y = 2x

On this interval,

2x \ge x^2

, hence:

\text{Area} = \int_0^1 (2x - x^2)\, dx

= \left[x^2 - \frac{x^3}{3}\right]_0^1 = 1 - \frac{1}{3} = \frac{2}{3}

Answer:

\frac{2}{3}

square unit, i.e. option B.

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