SOLUTION: Determine the following integral: The aria bound by the straight line y=x and tha parabola {{{ y=x^2}}}

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Question 287433: Determine the following integral: The aria bound by the straight line y=x and tha parabola +y=x%5E2
Answer by nabla(475) About Me  (Show Source):
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First, find where x=x^2 (this gives the end points of the closed interior). This occurs when 1=x and 0=x. So, we are interested in the closed interval [0,1].
Now, you will note by graphing that x>=x^2 throughout [0,1]. IE. .5>.25 etc.
So we integrate from 0 to 1 of (x-x^2)dx.
This is (x^2/2) -(x^3/3) evaluated from 0 to 1 so we have (1/2)-(1/3)=1/6.