What is the area bounded by the curves y = x^2 and y=the square root of x

Question

amistre64 · Answer

do you know the interval where they intesect?

amistre64 · Answer

$$\int_{a}^{b}f-g~dx$$

whpalmer4 · Answer

Solve $$x^2=\sqrt{x}$$ to find the endpoints of the integral.

anonymous · Answer

I don't understand how to do this, I need help working this out so I can use this as an example for the rest of my work

amistre64 · Answer

this is the help ... define the interval, and integrate the difference of the functions inbetween

amistre64 · Answer

if you get a negative value at the end, drop the sign

amistre64 · Answer

$$\left|\int_{a}^{b}x^2-x^{1/2}~dx\right|$$

whpalmer4 · Answer

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You find the two points where the curves cross to determine the endpoints of the integral.  The integral adds up all the infinitesimal rectangles from the function with the greater y value down to the function with the smaller y-value between the endpoints.