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BITSAT 2024

Exam: BITSAT
Year: 2024
Subject: Mathematics
Chapter: Area Under Curves

BITSAT 2024 · Mathematics · Area Under Curves

The area enclosed by the curves y=x^3 and y= x is

The area enclosed by the curves

y=x^3

and

y=\sqrt{x}

is

Options

A $\frac{5}{3}$ sq. units
B $\frac{5}{4}$ sq. units
C $\frac{5}{12}$ sq. unit
D $\frac{12}{5}$ sq. units

Correct answer

C. $\frac{5}{12}$ sq. unit

Step-by-step solution

Given curves are y=x^3 and

y=\sqrt{x}

Both curves intersects at

x=0 and x=1

Shaded region is required area

\begin{aligned} A & =\left|\int_0^1\left(x^3-\sqrt{x}\right) d x\right|=\left|\left[\frac{x^4}{4}-\frac{2 x^{3 / 2}}{3}\right]_0^1\right| \\ & =\left|\left[\frac{1}{4}-\frac{2}{3}\right]\right| \\ & =\frac{5}{12} \text{ sq. unit } \end{aligned}

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