TS EAMCET · Maths · Area Under Curves
The area (in sq. units) enclosed by the curves \(y=2 x-x^2\) and \(y=x^2-2 x-6\) is
- A \(\frac{64}{3}\)
- B \(\frac{8}{3}\)
- C \(\frac{128}{3}\)
- D \(\frac{16}{3}\)
Answer & Solution
Correct Answer
(A) \(\frac{64}{3}\)
Step-by-step Solution
Detailed explanation
Curves, \(y=2 x-x^2 \Rightarrow y=x^2-2 x-6\) Intersecting points, \(2 x-x^2=x^2-2 x-6\) \(2 x^2-4 x-6=0\) or \(x^2-2 x-3=0\) or \(\quad(x-3)(x+1)=0\) or \(x=-1, \quad x=3\) At \(x=-1, y=2 \times(-1)-(-1)^2=-3\) At \(x=3, y=-3\) So, both the curves are intersecting each other at…
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