Find the area of the region completely enclosed by the graphs of the given funct

Calculus
Tutor: None Selected Time limit: 1 Day

Aug 1st, 2015

Thank you for the opportunity to help you with your question!

To find the area of the region, first you must find where the two graphs intersect.  

This happens at x = 0 and 1.

Therefore the area is the integral of the top function - the bottom function from 0 to 1.  So we have:

Integral(sqrt x - x^2)dx.

If you have this ability on the graphing calculator, you can do it that way, or by hand we have:

2/3x^(3/2) - 1/3x^3 after integrating, then plugging in f(b) - f(a) for the interval (0,1) we have:

[2/3(1)^(3/2)] - 1/3(1)^3] - [2/3(0)^(3/2)] - 1/3(0)^3] = 2/3 - 1/3 

= 1/3 square units

Please let me know if you need any clarification. I'm always happy to answer your questions.
Aug 1st, 2015

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