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Definite Integrals & Area · Question 8 of 71

Question 8

MediumOriginal question

If ∫1c3x2 dx=26\int_1^c 3x^2\,dx = 26 and c>1c > 1, what is cc?

Options for question 8

Show the answer and explanation
CorrectNot quiteAnswer B

Correct answer: B

Explanation

  1. ∫1c3x2 dx=c3−1\int_1^c 3x^2\,dx = c^3 - 1.

  2. c3−1=26c^3 - 1 = 26 gives c3=27c^3 = 27, so c=3c = 3.

Worth noting

263\sqrt[3]{26} forgets to subtract the value at the lower limit, 13=11^3 = 1.

Concept
An unknown limit
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.