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Solve the given problems by integration.By a computer analysis, the electric current $i$ (in A) in a certain circuit is given by $i=\frac{0.0010\left(7 t^{2}+16 t+48\right)}{(t+4)\left(t^{2}+16\right)},$ where $t$ is the time (in s). Find the total charge that passes a point in the circuit in the first 0.250 s.
Calculus 1 / AB
Chapter 28
Methods of Integration
Section 10
Integration by Partial Fractions: Other Cases
Integrals
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University of Nottingham
Idaho State University
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honest question. Restart over 50 current equation. You need discharging capacitor my English Qatif. All right, So it I not istea maximum current in this case are the maximum current. Yes, actually was to the MF off the entire circuit. But by our or, you know that's, um f can be derived from the equation. Q equals two CV where ve stdm If so, it would be and Q is Q not and in the show Toto Toto church We close to see times he But, um if therefore this would be just goes to Oh, I see So disappear your not RC negative. You know, over RC times Exponential noted 50 of us and what we actually want to do is to find e power politics Peter Body resistor Given this ice cream are it's the instant in years pole at any given point in time t and therefore substitute I equals toe this for expression. All right, this is T We want to simplify this a little bit. Grouped together in common tones nature, diesel find expression gonna show that this is key. You will integrate this very to find what s T chota energy dissipated by the resistor so that be taking into Grew off Peter T t right From zero to infinity We take out the terms there are not dependent on time and there the rest will integrate. So infinity, the exponential terracotta cereal and a serially exponential chemical too One and f o E t zero tomb which is when it's one Abu we left and their b r c over to we left with not square over to see skc This expression were here It's the expression for the total energy It will stop, You know Sebesta. Thank you. Square over to see.
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