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AP EAMCET · Maths · Area Under Curves

Area of the region (in square units) enclosed by the curves \(y^2=8(x+2), y^2=4(1-x)\) and the Y -axis is

  1. A \(\frac{8}{3}(5-3 \sqrt{2})\)
  2. B \(\frac{8}{3}(\sqrt{2}-1)\)
  3. C \(\frac{8}{3}(3-\sqrt{2})\)
  4. D \(\frac{4}{3}(\sqrt{2}+1)\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{8}{3}(5-3 \sqrt{2})\)

Step-by-step Solution

Detailed explanation

\(y^2=8(x+2)\) \(y^2=4(1-x)\) The area of the required region is \(A=2\left[\int_{-2}^{-1} y_1 d x+\int_{-1}^0 y_2 d x\right]\) where \(y_1=\sqrt{8(x+2)}=2 \sqrt{2}(x+2)^{1 / 2}\) and \(y_2=\sqrt{4(1-x)}=2(1-x)^{1 / 2}\)…