The equation of a curve is such that $$\(\frac{\mathrm{d} y}{\mathrm{~d} x}=\frac{1}{(x-3)^{2}}+x\)$$. It is given that the curve passes through the point $$\((2,7)\)$$. Find the equation of the curve. ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................
Exam No：9709_w20_qp_11 Year：2020 Question No：2
Answer:
\((y=)\left[-(x-3)^{-1}\right]\left[+\frac{1}{2} x^{2}\right](+c)\)
\(7=1+2+c\)
\(y=-(x-3)^{-1}+\frac{1}{2} x^{2}+4\)
\(7=1+2+c\)
\(y=-(x-3)^{-1}+\frac{1}{2} x^{2}+4\)
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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