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Definite Integrals & Area · Question 14 of 71

Question 14

MediumOriginal question

Evaluate ∫0log⁡2e2x dx\int_{0}^{\log 2} e^{2 x}\,dx.

Options for question 14

Show the answer and explanation
CorrectNot quiteAnswer C

Correct answer: C

Explanation

  1. An antiderivative is F(x)=e2x2F(x) = \frac{e^{2 x}}{2}.

  2. By the fundamental theorem, the integral is F(log⁡2)−F(0)=32F(\log 2) - F(0) = \frac{3}{2}.

Worth noting

22 is F(log⁡2)F(\log 2) alone: F(0)F(0) was not subtracted.

Concept
A definite integral of an exponential
Typical time
90 s
Your time
—
The rule this testsThe fundamental theorem of calculus
Practise this chapter →

Ten questions from Definite Integrals & Area, at your own pace.

Practise this chapter →

Ten questions from Definite Integrals & Area, at your own pace.