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) \(y = - \frac { 8 } { x } + \frac { 5 } { 4 } \tan ^ { - 1 } \left( \frac { 3 } { 4 } x \right) + 10 - \frac { 5 } { 24 } \pi\)

---

Definitions:

Stereotype Threat

The risk of confirming negative stereotypes about an individual's racial, ethnic, gender, or cultural group, which can hinder performance in a variety of settings.

Master Status

An individual’s most significant status, which often overshadows all other social positions they may occupy.

Stigmatizing Attribute

A characteristic of a person that is socially devalued or discredited, leading to stigma or discrimination.

Total Self

The complete set of characteristics, values, beliefs, and abilities that make up an individual's identity.