AP EAMCET · Maths · Area Under Curves
If \((\alpha, \beta)\) is the stationary point of the curve \(y=2 x-x^2\), then the area bounded by the curves \(y=2 x, y=2 x-x^2, x=0\) and \(x=\alpha\) is
- A \(\frac{3 \log 2+4}{2}\)
- B \(\frac{3+\log 4}{6}\)
- C \(\frac{3-\log 4}{3 \log 2}\)
- D \(\frac{1}{\log 2}+\frac{3}{4}\)
Answer & Solution
Correct Answer
(C) \(\frac{3-\log 4}{3 \log 2}\)
Step-by-step Solution
Detailed explanation
\(y=2 x-x^2\) For stationary point \(\frac{d y}{d x}=0\) \(\Rightarrow 2-2 x=0 \Rightarrow x=1=\alpha\) Given curves are \(y=2^{\mathrm{x}}, y=2 x-x^2, x=0, x=1\)…
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