Solve the problem by integration.
-By a computer analysis, the electric current i (in A) in a certain circuit is given by i $= \frac { 0.0040 \left( 8 t ^ { 2 } + 15 t + 75 \right) } { ( t + 5 ) \left( t ^ { 2 } + 15 \right) }$, where $t$ is the time (in s). Find the total charge that passes a point in the circuit in the first $0.25 \mathrm {~s}$.
A) 0.0002 C
B) 0.0051 C
C) 0.0010 C
D) 0.0049 C

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The Answer of Solve the problem by integration.
-By a computer analysis, the electric current i (in A) in a certain circuit is given by i $= \frac { 0.0040 \left( 8 t ^ { 2 } + 15 t + 75 \right) } { ( t + 5 ) \left( t ^ { 2 } + 15 \right) }$, where $t$ is the time (in s). Find the total charge that passes a point in the circuit in the first $0.25 \mathrm {~s}$.
A) 0.0002 C
B) 0.0051 C
C) 0.0010 C
D) 0.0049 C

Solve the Problem by Integration =0.0040(8t2+15t+75)(t+5)(t2+15)= \frac { 0.0040 \left( 8 t ^ { 2 } + 15 t + 75 \right) } { ( t + 5 ) \left( t ^ { 2 } + 15 \right) }=(t+5)(t2+15)0.0040(8t2+15t+75)​

Solve the Problem by Integration $= \frac { 0.0040 \left( 8 t ^ { 2 } + 15 t + 75 \right) } { ( t + 5 ) \left( t ^ { 2 } + 15 \right) }$