WBJEE · Maths · Area Under Curves
The area bounded by the parabolas \(y=4 x^{2}, y=\frac{x^{2}}{9}\) and the straight line \(y=2\) is
- A \(\frac{20 \sqrt{2}}{3}\) sq. unit
- B \(10 \sqrt{5}\) sq. unit
- C \(\frac{10 \sqrt{3}}{7}\) sq. unit
- D \(10 \sqrt{2}\) sq. unit
Answer & Solution
Correct Answer
(A) \(\frac{20 \sqrt{2}}{3}\) sq. unit
Step-by-step Solution
Detailed explanation
\(y=4 x^{2}, y=\frac{x^{2}}{9}, y=2\) \(A=2 \int_{0}^{2}\left(3 \sqrt{y}-\frac{\sqrt{y}}{2}\right) d y=2 \int_{0}^{2} \frac{5 \sqrt{y}}{2} d y=\left.5 \frac{y^{3 / 2}}{3 / 2}\right|_{0} ^{2}=\frac{10}{3}\left[2^{3 / 2}\right]=\frac{20 \sqrt{2}}{3}\)
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