Given-d-5t-4-2-dt-10g-t-Find-1-k-g-t-dt-in-terms-of-k-where-k-is-a-constant-

Question Number 121775 by ZiYangLee last updated on 11/Nov/20

Given \frac{d {(5 t - 4)}^{2}}{d t} = 10 g (t) .

Find \int_{1}^{k} g (t) d t in terms of k, where k

is a constant .

Answered by Dwaipayan Shikari last updated on 11/Nov/20

\int_{1}^{k} d u = \int_{1}^{k} 10 g (t) d t u = {(5 t - 4)}^{2}

{[u]}_{1}^{k} = 10 \int_{1}^{k} g (t) d t

\frac{1}{10} ({(5 k - 4)}^{2} - 1) = \int_{1}^{k} g (t) d t = \frac{5}{2} k^{2} - 4 k + \frac{3}{2}