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The current in a wire varies with time a...

The current in a wire varies with time according to the relation i = `2.0A + (0.6A//s^(2))t^(2)`. How many coulomb of charge pass a cross-section of the wire in the time interval between t = 0 and t = 10s?

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(a) ` q = int_(0)^(t) idt = int_(0)^(10s) [ 2.0 A + (0.6As^(-2))t^(2)]dt`
` = [(2.0A)t + (0.6 As^(-2))(t^(3))/(3)]_(0)^(10s)`
` = (2.0A) (10s) + (0.6 As^(-2)) ((10s)^(3))/(3) = 20 As + 200 As `
` = 220As ` = 220 coulomb .
(b) Constant current ` i = (q)/(t) = (220 C)/(10 s) = 22 A`
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