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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

  1. A \(\frac{32}{3}\)
  2. B \(\frac{16}{3}\)
  3. C \(\frac{64}{3}\)
  4. D \(\frac{128}{3}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\frac{64}{3}\)

Step-by-step Solution

Detailed explanation

\(x^2 = 8-x^2 \Rightarrow 2x^2=8 \Rightarrow x^2=4 \Rightarrow x = \pm 2\) \(A = \int_{-2}^{2} ((8-x^2) - x^2) dx\) \(A = \int_{-2}^{2} (8-2x^2) dx = [8x - \frac{2x^3}{3}]_{-2}^{2}\)…