AP EAMCET · Maths · Area Under Curves
The area (in sq.units) of the region bounded by the curves \(y=x^2\) and \(y=8-x^2\) is
- A \(\frac{32}{3}\)
- B \(\frac{16}{3}\)
- C \(\frac{64}{3}\)
- D \(\frac{128}{3}\)
Answer & Solution
Correct Answer
(C) \(\frac{64}{3}\)
Step-by-step Solution
Detailed explanation
\(x^2 = 8-x^2 \Rightarrow 2x^2=8 \Rightarrow x^2=4 \Rightarrow x = \pm 2\) \(A = \int_{-2}^{2} ((8-x^2) - x^2) dx\) \(A = \int_{-2}^{2} (8-2x^2) dx = [8x - \frac{2x^3}{3}]_{-2}^{2}\)…
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