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

Question

Quizplus · Accepted Answer

Since we are only given the function without any limits of integration, let us assume the limits to be from 0 to x.

Then, according to Part I of the Fundamental Theorem of Calculus, the value of the definite integral is the difference between the antiderivative of the upper limit and the antiderivative of the lower limit.

Thus,

∫(0 to x) e^(2t) dt = [1/2 e^(2t)] from 0 to x
= 1/2 [(e^(2x)) - (e^0)]
= 1/2 (e^(2x) - 1)

Therefore, the correct option is B.

Use Part I of the Fundamental Theorem of Calculus to Compute