Question
Find the area between the curve and its asymptote parallel to y-axis.
Answer :
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The given curve is (y^2(4-x)=x^3), or (y^2=\dfrac{x^3}{4-x}). As (x\to 4^{-}), the denominator tends to zero and (|y|\to\infty), so the asymptote parallel to the (y)-axis is (x=4). The curve exists for (0\le x<4) and is symmetric about the (x)-axis. The area between the curve
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