Question on Integrating a Given Function

Here is a Multi choice question to Evaluate function by Integration.
You can find similar set of questions at TutorVista Blogs.

Topic : Integrating a Function.

Below example will help you to identify correct choice and get reasons for, why remaining choices are incorrect.

Question : At what point in the interval [0, √3] does the function y=x² - 1 assumes its average value.
a. -1
b. 1
c. 1.5
d. 1.7

Solution :
Choice b is correct.
Average value = 1/(√3 - 0)₀∫^√3 (x² - 1)dx = 0
And x² – 1 = 0
Therefore, y= x² -1 assumes its average at x = 1

Choice a is incorrect as -1 is not in the interval [0, √3]

Choice c is incorrect as 1.5 does not satisfy the equation x² -1=0

Choice d is incorrect as 1.7 does not satisfy the equation x² -1=0


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