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Find a real number a with the property that the area bounded by y = ax^2 and y = ax is 1/2 square units.

Calculus II Question

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I think its A=3

you are finding the area between curves here so you first find the interval of the problem by setting the equations equal to one another and factoring to find the roots:

y=ax^2 y=ax

ax^2=ax ax^2-ax=0 (x-1)(ax)=0 your roots are at 0 and 1 this is your interval

Then you integrate the top curve (y=ax) on the interval of 0 to 1 and subract the integral of the bottom curve. This gives you the area between the curve. You will end up with this equation:

a/2-a/3=1/2 (set equal to your desired area)

solve for a... a=3

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