TS EAMCET · Maths · Area Under Curves
If the area of the region enclosed by the curve \(a y=x^2\) and the line \(x+y=2 a\) is \(k a^2\), then \(k=\)
- A \(\frac{2}{9}\)
- B \(\frac{9}{2}\)
- C \(\frac{3}{2}\)
- D \(\frac{2}{3}\)
Answer & Solution
Correct Answer
(B) \(\frac{9}{2}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & x+y=2 a, a y=x^2 \\ & x+\frac{x^2}{a}=2 a\end{aligned}\) \(\begin{aligned} & a x+x^2-2 a^2=0 \\ & (x+2 a)(x-a)=0 \Rightarrow x=a,-2 a \text { and } y=a, 4 a\end{aligned}\) Area \(=\int_{-2 a}^a\left(2 a-x-\frac{x^2}{a}\right) d x\)…
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