Solve the Problem by Integration $\frac { 4 x + 4 } { x ^ { 2 } + 4 x }$

question 145

Multiple Choice

Solve the problem by integration.
-The general expression for the slope of a curve is $\frac { 4 x + 4 } { x ^ { 2 } + 4 x }$ . Find the equation of the curve if it passes through (1, 0 ) .

• A) \(y = \ln \left| \frac { x ( x - 4 ) ^ { 3 } } { 125 } \right|\)
• B) \(y = \ln \left| \frac { x ( x + 4 ) ^ { 3 } } { 5 } \right|\)
• C) \(y = \ln \left| x ( x + 4 ) ^ { 3 } \right|\)
• D) \(y = \ln \left| \frac { x ( x + 4 ) ^ { 3 } } { 125 } \right|\)

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Definitions:

Counterweights

Weights used to balance rotating parts in machinery, ensuring smooth operation and reducing vibration.

Out-of-phase

A condition in which two or more periodic signals (waveforms) do not align properly in time, potentially causing interference or reduced performance in systems such as electrical or audio applications.

Slip Splines

Used on a drive shaft (propeller shaft) stub and yoke assembly to permit variations in length caused by frame and suspension oscillations while transmitting drive torque.

Transmission Yoke

A mechanical component that connects the transmission output shaft to the driveshaft in a vehicle, allowing for the transfer of torque.