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


label Calculus
account_circle Unassigned
schedule 1 Day
account_balance_wallet $5

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

Did you know? You can earn $20 for every friend you invite to Studypool!
Click here to
Refer a Friend
...
Aug 1st, 2015
...
Aug 1st, 2015
Nov 24th, 2017
check_circle
Mark as Final Answer
check_circle
Unmark as Final Answer
check_circle
Final Answer

Secure Information

Content will be erased after question is completed.

check_circle
Final Answer