COMEDK · Maths · 31. Area Under Curves
The area of the region bound by the curves \(y=x^{2}\) and \(y=4 x-x^{2}\) is
- A \(\frac{16}{3}\) sq. units
- B \(\frac{8}{3}\) sq. units
- C \(\frac{4}{3}\) sq. units
- D \(\frac{2}{3}\) sq. unit
Answer & Solution
Correct Answer
(B) \(\frac{8}{3}\) sq. units
Step-by-step Solution
Detailed explanation
Given equation of curves are \(y=x^{2}\) and \(\begin{aligned} y &=4 x-x^{2} \\ y-4 &=-4+4 x-x^{2} \\ y-4 &=-\left(x^{2}-4 x+4\right)=-(x-2)^{2} \end{aligned}\) Now, required area \(=\int_{0}^{2}\left\{\left(4 x-x^{2}\right)-x^{2}\right\} d x\)…
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