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Definite Integrals & Area · Question 6 of 71

Question 6

MediumOriginal question

Evaluate ∫0log⁡3ex dx\int_{0}^{\log 3} e^{x}\,dx.

Options for question 6

Show the answer and explanation
CorrectNot quiteAnswer D

Correct answer: D

Explanation

  1. An antiderivative is F(x)=exF(x) = e^{x}.

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

Worth noting

33 is F(log⁡3)F(\log 3) 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.