MHT CET · Maths · Area Under Curves
The area of the region bounded by the parabola \(y=x^2\) and the curve \(y=|x|\) is
- A \(\frac{1}{2}\) sq. units
- B \(\frac{1}{3}\) sq. units
- C \(\frac{1}{4}\) sq. units
- D \(\frac{1}{6}\) sq. units
Answer & Solution
Correct Answer
(B) \(\frac{1}{3}\) sq. units
Step-by-step Solution
Detailed explanation
\(\begin{aligned} \text {Required area } & =2 \int_0^1\left(x-x^2\right) \mathrm{d} x \\ & =2\left[\frac{x^2}{2}-\frac{x^3}{3}\right]_0^1 \\ & =2\left(\frac{1}{2}-\frac{1}{3}\right)=\frac{1}{3} \text { sq.units }\end{aligned}\)
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