TS EAMCET · Maths · Area Under Curves
The area (in sq. units) bounded by the curve \(y=2 x-x^2\) and the line \(y=-x\) is
- A \(\frac{9}{2}\)
- B \(\frac{11}{2}\)
- C \(\frac{16}{3}\)
- D \(\frac{22}{5}\)
Answer & Solution
Correct Answer
(C) \(\frac{16}{3}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text { Area }=\int_0^3\left(2 x-x^2\right) d x-\int_0^3-x d x \\ & =\int_0^3\left(3 x-x^2\right) d x=\left[\frac{3 x^2}{2}-\frac{x^3}{3}\right]_0^3 \\ & =\frac{27}{2}-\frac{27}{3}=\frac{27}{6}=\frac{9}{2}\end{aligned}\)
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