MHT CET · Maths · Area Under Curves
The area bounded by the parabola \(y^2=x\), the straight line \(y=4\) and \(\mathrm{Y}\) axis is
- A \(2 \sqrt{7}\) sq. unit
- B \(\frac{64}{3}\) sq. units
- C \(\frac{16}{3}\) sq. units
- D \(7 \sqrt{2}\) sq. units
Answer & Solution
Correct Answer
(B) \(\frac{64}{3}\) sq. units
Step-by-step Solution
Detailed explanation
Refer figure
Required area is shaded.
Point of intersection of \(y^2=x\) and \(y=4\) is \(A \equiv(16,4)\)
\(
\begin{aligned}
\therefore A & =\int_0^4 y^2 d y \\
& =\left[\frac{y^3}{3}\right]_0^4=\frac{64}{3} \text { sq. units }
\end{aligned}
\)
Required area is shaded.
Point of intersection of \(y^2=x\) and \(y=4\) is \(A \equiv(16,4)\)
\(
\begin{aligned}
\therefore A & =\int_0^4 y^2 d y \\
& =\left[\frac{y^3}{3}\right]_0^4=\frac{64}{3} \text { sq. units }
\end{aligned}
\)
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