SOLUTION: Find the area between the curves y = x² and y = x + 12. Round your answer to one decimal place.

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Question 1115245: Find the area between the curves y = x² and y = x + 12.
Round your answer to one decimal place.
Answer by ikleyn(52855) About Me  (Show Source):
You can put this solution on YOUR website!
.
1.  Step 1.  Find intersection points.

   
    For it, solve the equation  x^2 = x + 12.


    x^2 - x -12 = 0  ====>  x = 4  and  x= -3.




2.  Step 2.

    Over the interval [-3,4],  the upper curve is  y = x + 12;  the lower curve is  y = x^2.


    Hence, you need to take the integral of the difference  (x+12) - x^2  from  -3  to  4.



    


    Plot y = x + 12 (red) and  y = x^2 (green)




3.  I just explained EVERYTHING to you.  The rest is just arithmetic, which I leave to you.