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Derivatives and Integrals

1.) The current in a circuit is i = 2.00 cos 100t. Find the voltage across a 100-microfarad(uF) capacitor after 0.200 s, if the initial voltage is Zero (one microfarad(uF)=10 to the power of -6 F).

2.) Find the volume of the solid of revolution obtained by rotating the region bounded by y = cos x to the power 2, x=0, x = square root of (pi/2) and y = 0 about the y - axis.

3.) The voltage in a certain circuit is given by e(t) = E sin wt . Find the mean voltage over half a period.

Solution Preview

Questions (Chapter 7 Integration Techniques).

1.) The current in a circuit is i = 2.00 cos 100t. Find the voltage across a 100-microfarad(uF) capacitor after 0.200 s, if

the initial voltage is Zero (one microfarad(uF)=10 to the power of -6 F).

i = C dv/dt
2 Cos (100t) = 10^(-4) * dv/dt
dv = 20000 Cos (100t) dt
Integrate both sides,
v = (20000/100) Sin (100t) + K
at t=0, V = 0 ==> K = 0
Hence, v(t) = 200 Sin (100t)
at t=0.2 sec, v = 200 Sin(20 Radians) = ...

Solution Summary

Derivatives and integrals are found.

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