Evaluate the Integral $$\int _ { 0 } ^ { 1 / 2 } 12 x \cos \pi x d x$$

question 131

Short Answer

Evaluate the integral.
$$\int _ { 0 } ^ { 1 / 2 } 12 x \cos \pi x d x$$

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Definitions:

Torque Reduction

A process or mechanism by which torque output, particularly in an engine or drivetrain, is intentionally decreased to prevent damage or improve control.

Driven Gear

A gear that receives power from another gear or rotating component in a mechanical system.

Auxiliary Section

An additional section of a device or system that provides supplementary functions or capabilities.

Gear Ratios

The ratio between the numbers of teeth on two gears that are meshed or connected, affecting speed and torque in mechanical systems.