A current through a wire depends on time as i = α 0 t + β t 2 , where α 0 = 20 A s - 1 and β = 8 A s - 2 . Find the charge crossed through a section of the wire in 15 s .

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i = 20 t + 8 t 2 i = d q d t ⇒ ∫ d q = ∫ i d t ⇒ q = ∫ 0 15 20 t + 8 t 2 d t q = 20 t 2 2 + 8 t 3 3 0 15 q = 10 × 15 2 + 8 15 3 3 q = 2250 + 9000 q = 11250 C

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