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Definite Integrals & Area · Question 35 of 71

Question 35

EasyOriginal question

∫05f(x) dx=4\int_0^5 f(x)\,dx = 4 and ∫02f(x) dx=−2\int_0^2 f(x)\,dx = -2. What is ∫25f(x) dx\int_2^5 f(x)\,dx?

Options for question 35

Show the answer and explanation
CorrectNot quiteAnswer D

Correct answer: D

Explanation

  1. ∫05f=∫02f+∫25f\int_0^5 f = \int_0^2 f + \int_2^5 f.

  2. So ∫25f=4−(−2)=6\int_2^5 f = 4 - (-2) = 6.

Worth noting

2 adds the two given values instead of subtracting one from the other.

Concept
Splitting the interval
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.