WBJEE · Maths · Area Under Curves
The straight line through the origin which divides the area formed by the curves \(y=2 x-x^{2}, y=0\) and \(x=1\) into two equal halves is
- A \(y=x\)
- B \(y=2 x\)
- C \(y=\frac{3}{2} x\)
- D \(y=\frac{2}{3} x\)
Answer & Solution
Correct Answer
(D) \(y=\frac{2}{3} x\)
Step-by-step Solution
Detailed explanation
\(y=2 x-x^{2}, y=0, x=1\) Area \(=A=\int_{0}^{1}\left(2 x-x^{2}\right) d x\) or, \(A=\frac{2}{3}\) sq units Let \(y=m x\) line divides area in two equal halves \(\therefore \frac{1}{2} \times 1 \times \mathrm{m}=\frac{1}{3}\) or, \(\mathrm{m}=\frac{2}{3} \therefore\) equation of…
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