MHT CET · Maths · Area Under Curves
The area bounded by the parabola \(y^{2}=x\), straight line \(y=4\) and \(y\) -axis is square units is
- A \(16 / 3\) sq. unit
- B \(64 / 3\) sq. unit
- C \(7 \sqrt{2}\) sq. unit
- D None of these
Answer & Solution
Correct Answer
(B) \(64 / 3\) sq. unit
Step-by-step Solution
Detailed explanation
Line \(y=4\) meets the parabola \(y^{2}=x\) at \(A\)
\(\therefore \quad 16=x\) and \(A\) is \((16,4)\)
\(\therefore\) Required area
\(
\begin{array}{l}
=\int_{y=0}^{4} x d y \\
=\int_{y=0}^{4} y^{2} d y \\
=\left[y^{3} / 3\right]_{0}^{4} \\
=\frac{64}{3} \text { sq units }
\end{array}
\)
\(\therefore \quad 16=x\) and \(A\) is \((16,4)\)
\(\therefore\) Required area
\(
\begin{array}{l}
=\int_{y=0}^{4} x d y \\
=\int_{y=0}^{4} y^{2} d y \\
=\left[y^{3} / 3\right]_{0}^{4} \\
=\frac{64}{3} \text { sq units }
\end{array}
\)
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