Integration

Question

Given that:

t
∫ (3X + 2) dx = (13/2)
1

Find the value of t

Answer 1

(3/2)x^2 + 2x | from 1 to t
= (3/2)t^2 + 2t - (3/2 + 2) = 13/2
(3/2)t^2 + 2t - 10 = 0
3t^2 + 4t - 20 = 0
(t - 2)(3t + 10) = 0

t = 2 or t = -10/3

depending on what interpretation is given to the integral, we might reject the t = -10/3