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Definite Integrals & Area · Question 13 of 71

Question 13

MediumOriginal question

Evaluate ∫031x+1 dx\int_{0}^{3} \frac{1}{x + 1}\,dx.

Options for question 13

Show the answer and explanation
CorrectNot quiteAnswer D

Correct answer: D

Explanation

  1. An antiderivative is F(x)=log⁡(x+1)F(x) = \log{\left(x + 1 \right)}.

  2. By the fundamental theorem, the integral is F(3)−F(0)=log⁡4F(3) - F(0) = \log 4.

Worth noting

−log⁡4- \log 4 subtracts the wrong way, F(0)−F(3)F(0) - F(3).

Concept
A definite integral of 1/x
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.