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Definite Integrals & Area · Question 37 of 71

Question 37

EasyOriginal question

If ∫03f(x) dx=5\int_0^3 f(x)\,dx = 5 and ∫03g(x) dx=2\int_0^3 g(x)\,dx = 2, what is ∫03(3f(x)−2g(x))dx\int_0^3 \left(3f(x) - 2g(x)\right)dx?

Options for question 37

Show the answer and explanation
CorrectNot quiteAnswer C

Correct answer: C

Explanation

  1. The integral is linear: 3∫03f dx−2∫03g dx3\int_0^3 f\,dx - 2\int_0^3 g\,dx.

  2. 3×5−2×2=113 \times 5 - 2 \times 2 = 11.

Worth noting

3 is 5−25 - 2, leaving out the multipliers 3 and 2.

Concept
Linearity of the definite integral
Typical time
60 s
Your time
—
The rule this testsProperties of definite integrals
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.