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Area of Bounded Regions · Question 68 of 115

Question 68

MediumOriginal question

For which a>0a > 0 is the area under y=x2y = x^{2} from x=0x = 0 to x=ax = a equal to 9 square units?

Options for question 68

Show the answer and explanation
CorrectNot quiteAnswer B

Correct answer: B

Explanation

  1. ∫0ax2 dx=a33=9\int_0^{a} x^{2}\,dx = \frac{a^{3}}{3} = 9.

  2. a3=27a^{3} = 27, so a=3a = 3.

Worth noting

27 is a3a^{3}; the cube root is still to be taken.

Concept
Working back from an area
Typical time
90 s
Your time
—
The rule this testsParabolas
Practise this chapter →

Ten questions from Area of Bounded Regions, at your own pace.

Practise this chapter →

Ten questions from Area of Bounded Regions, at your own pace.