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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Definitions:

Vertebral Column

The backbone or spine, consisting of a series of vertebrae that protect the spinal cord and provide structural support.

Skull

The bony structure forming the head, supporting the structures of the face and protecting the brain.

Zygomatic Arch

The arch of bone that forms from the temporal process of the zygomatic bone and the zygomatic process of the temporal bone, creating the prominence of the cheek.

Zygomatic Process

A bony projection of the temporal bone that articulates with the zygoma (cheekbone) to form part of the cheek structure.