A curve is such that $$\(\frac{\mathrm{d} y}{\mathrm{~d} x}=\frac{8}{(3 x+2)^{2}}\)$$. The curve passes through the point $$\(\left(2,5 \frac{2}{3}\right)\)$$. Find the equation of the curve. ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................
Exam No：9709_w21_qp_12 Year：2021 Question No：4
Answer:
\(y=-\frac{\frac{8}{3}}{(3 x+2)}[+c]\)
\(5 \frac{2}{3}=-\frac{\frac{8}{3}}{(3 \times 2+2)}+c\)
\(y=-\frac{8}{3(3 x+2)}+6\)
\(5 \frac{2}{3}=-\frac{\frac{8}{3}}{(3 \times 2+2)}+c\)
\(y=-\frac{8}{3(3 x+2)}+6\)
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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