A Simple Word Problem on Finding an Integral of an Expression

Here is a Multi choice word problem to Evaluate the value of x by Integration. You can find similar set of questions at TutorVista Blogs.

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

Question : The marginal cost of printing a poster when x posters have been printed is dc/dx = 1/2√x Dollars, then the cost of printing posters 101 to 400 is
a. $5
b. $10
c. $15
d. $20

Solution :Choice b is correct.The cost of printing posters 101 to 400 is
C(400)-C(100)

=₁₀₀∫⁴⁰⁰(dc/dx)dx

=₁₀₀∫⁴⁰⁰(1/2√x)dx

= 10

Choice a is incorrect as the value of the integral ₁₀₀∫⁴⁰⁰(1/2√x)dx is not equal to 10.

Choice c is incorrect as the value of the ₁₀₀∫⁴⁰⁰(1/2√x)dx is not equal to 15.

Choice d is incorrect as the value of the integral is not equal to 20.