MHT CET · Maths · Area Under Curves
The area of the region bounded by the curve \(\mathrm{y}=x^{2}+1\), the lines \(\mathrm{x}=1, \mathrm{x}=2\) and the \(\mathrm{X}\) - axis is
- A \(\frac{13}{3}\) sq. units
- B \(\frac{10}{3}\) sq. units
- C \(\frac{16}{3}\) sq. units
- D \(\frac{19}{3}\) sq. units
Answer & Solution
Correct Answer
(B) \(\frac{10}{3}\) sq. units
Step-by-step Solution
Detailed explanation
\(\begin{aligned} A &=\int_{1}^{2}\left(x^{2}+1\right) d x \\ &=\left[\frac{x^{3}}{3}+x\right]_{1}^{2}=\left(\frac{8}{3}+2\right)-\left(\frac{1}{3}+1\right)=\frac{10}{3} \end{aligned}\)
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