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Integration help

0 votes

asked Jun 28, 2015 in CALCULUS by anonymous

1 Answer

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Step 1:

Alternating sinusoidal current function is .

Where, is amplitude, is the time and is the phase.

For alternating current, the differential amount of heat  by joule-lenz law is image.

Find the quantity of heat released by alternating sinusoidal current during a cycle image in a conductor by integrating above expression.

image.

Substitute image in above expression.

image

Step 2:

Double angle  identity: image.

image

image

image

Therefore, heat released by alternating sinusoidal current during a cycle image in a conductor is image.

Solution:

Heat released by alternating sinusoidal current during a cycle image in a conductor is image.

answered Jun 29, 2015 by cameron Mentor
edited Jun 29, 2015 by bradely

Please explain:

 

 

Consider image.

Rewrite the expression as image.

Trigonometric property: image.

image

Trigonometric property: image.

image.

Hence image

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