MHT CET · Maths · Area Under Curves
The area (in square units) in the first quadrant bounded by the curve \(y=x^2+2\) and the lines \(y=x+1, x=0\) and \(x=3\), is
- A \(\frac{15}{4}\)
- B \(\frac{21}{2}\)
- C \(\frac{17}{4}\)
- D \(\frac{15}{2}\)
Answer & Solution
Correct Answer
(D) \(\frac{15}{2}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} \text { Required area } & =\int_0^3\left(x^2+2\right)-(x+1) \mathrm{d} x \\ & =\int_0^3\left(x^2-x+1\right) \mathrm{d} x \\ & =\left[\frac{x^3}{3}-\frac{x^2}{2}+x\right]_0^3=\frac{15}{2} \text { sq. units }\end{aligned}\)
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