MHT CET · Maths · Area Under Curves
The area bounded by the curve \(y^2=2 x+1\) and the line \(x-y=1\) is
- A \(\frac{2}{3}\) sq. units
- B \(\frac{4}{3}\) sq. units
- C \(\frac{8}{3}\) sq. units
- D \(\frac{16}{3}\) sq. units
Answer & Solution
Correct Answer
(D) \(\frac{16}{3}\) sq. units
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text { Required area }=\int_{-1}^3\left\{(1+y)-\left(\frac{y^2-1}{2}\right)\right\} \mathrm{d} y \\ & =\int_{-1}^3\left(\frac{3}{2}+y-\frac{y^2}{2}\right) \mathrm{d} y \\ & =\left[\frac{3}{2} y+\frac{y^2}{2}-\frac{y^3}{6}\right]_{-1}^3 \\ & =\left(\frac{9}{2}+\frac{9}{2}-\frac{27}{6}\right)-\left(\frac{-3}{2}+\frac{1}{2}+\frac{1}{6}\right)=\frac{16}{3}\end{aligned}\)
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