MHT CET · Maths · Area Under Curves
Area of the region bounded by the curve \(y=x^2+2\) and the lines \(y=x, x=0\) and \(x=3\) is
- A \(\frac{19}{2}\) sq \(\cdot\) units
- B \(\frac{21}{2} \mathrm{sq} \cdot\) units
- C \(15 s q \cdot\) units
- D \(\frac{9}{2} \mathrm{sq} \cdot \mathrm{units}\)
Answer & Solution
Correct Answer
(B) \(\frac{21}{2} \mathrm{sq} \cdot\) units
Step-by-step Solution
Detailed explanation
\(\text { Required area }=\int_0^3\left(x^2+2-x\right) d x=\) \(\left[\frac{x^3}{3}+2 x-\frac{x^2}{2}\right]_0^3\)
\(=\frac{27}{3}+6-\frac{9}{2}=\frac{21}{2}\)
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