Use Part I of the Fundamental Theorem of Calculus to compute the integral exactly.

Question

Quizplus · Accepted Answer

Let F(x) = ∫(1, x) e^(t^2) dt
By the Fundamental Theorem of Calculus, F'(x) = e^(x^2)
Therefore, ∫(1, 3) e^(x^2) dx = F(3) - F(1) = ∫(1, 3) e^(t^2) dt - ∫(1, 1) e^(t^2) dt
The second integral is 0. 
Thus, the answer is F(3) = ∫(1, 3) e^(t^2) dt, which is equal to approximately 6.838. 
The closest option to this value is B, which is 6.839.

Use Part I of the Fundamental Theorem of Calculus to Compute