Solve the Problem by Integration $\frac { \mathrm { dy } } { \mathrm { dx } } = \frac { 87 \mathrm { x } ^ { 2 } + 128 } { 9 x ^ { 4 } + 16 \mathrm { x } ^ { 2 } }$

question 334

Multiple Choice

Solve the problem by integration.
-The slope of a curve is given by $\frac { \mathrm { dy } } { \mathrm { dx } } = \frac { 87 \mathrm { x } ^ { 2 } + 128 } { 9 x ^ { 4 } + 16 \mathrm { x } ^ { 2 } }$ . Find the equation of the curve if it passes through $\left( \frac { 4 } { 3 } , 4 \right)$ .

• A) \(y = \frac { 8 } { x } - \frac { 5 } { 4 } \tan ^ { - 1 } \left( \frac { 3 } { 4 } x \right) - 10 + \frac { 5 } { 24 } \pi\)
• B) \(y = - \frac { 8 } { x } + \frac { 5 } { 4 } \tan ^ { - 1 } \left( \frac { 3 } { 4 } x \right) + 10 - \frac { 5 } { 16 } \pi\)
• C) \(y = \frac { 8 } { x } + \frac { 5 } { 4 } \tan ^ { - 1 } \left( \frac { 3 } { 4 } x \right) - 10 - \frac { 5 } { 16 } \pi\)
• D) \(y = - \frac { 8 } { x } + \frac { 5 } { 4 } \tan ^ { - 1 } \left( \frac { 3 } { 4 } x \right) + 10 - \frac { 5 } { 24 } \pi\)

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