The equation of a curve is such that $$\(\frac{\mathrm{d} y}{\mathrm{~d} x}=3 x^{\frac{1}{2}}-3 x^{-\frac{1}{2}}\)$$. It is given that the point $$\((4,7)\)$$ lies on the curve. Find the equation of the curve. ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................
Exam No：9709_s20_qp_13 Year：2020 Question No：2
Answer:
\((y)=\frac{3 x^{\frac{3}{2}}}{\frac{3}{2}}-\frac{3 x^{\frac{1}{2}}}{\frac{1}{2}}(+c)\)
\(7=16-12+c\)
(M1 for subsituting \(x=4, y=7\) into their integrated expansion)
\(y=2 x^{\frac{3}{2}}-6 x^{\frac{1}{2}}+3\)
\(7=16-12+c\)
(M1 for subsituting \(x=4, y=7\) into their integrated expansion)
\(y=2 x^{\frac{3}{2}}-6 x^{\frac{1}{2}}+3\)
Knowledge points:
1.8.1 understand integration as the reverse process of differentiation, and integrate (for any rational n except-1 , together with constant multiples, sums and differences
1.8.2 solve problems involving the evaluation of a constant of integration
Solution:
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