MHT CET · Maths · Area Under Curves
The area of the region, bounded by the parabola \(y=x^2+2\) and the lines \(y=x, x=0\) and \(x=3\), is
- A \(\frac{9}{2}\) sq. units
- B \(\frac{11}{2}\) sq. units
- C \(\frac{15}{2}\) sq. units
- D \(\frac{21}{2}\) sq. units
Answer & Solution
Correct Answer
(D) \(\frac{21}{2}\) sq. units
Step-by-step Solution
Detailed explanation
\(\begin{aligned} \text { Required area } & =\int_0^3\left(x^2+2-\dot{x}\right) \mathrm{d} x \\ & =\left[\frac{x^3}{3}+2 x-\frac{x^2}{2}\right]_0^3 \\ & =9+6-\frac{9}{2}-0 \\ & =\frac{21}{2} \text { sq. unit }\end{aligned}\)
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