Which choice gives the area under t^2 between t = 2 and t = x as a function of x?

Question

anonymous · Answer

attachment

mertsj · Answer

The third one

anonymous · Answer

Can you tell me how you did that?

mertsj · Answer

The area under the curve is the integral of the function.  The function is t^2 so it is the integral of t^2 with respect to t.  The boundaries are from 2 to x.  The lesser boundary is given first and goes at the bottom of the integral sign.

anonymous · Answer

How did you determine that it was with respect to x?

anonymous · Answer

*as a function of x

mertsj · Answer

I said that the integral is with respect to t not with respect to x.  You will end up with a function of x after you integrate and substitute x in for t as x is the upper boundary.

anonymous · Answer

oh, so that's what they mean as a function of x.  Thanks!

anonymous · Answer

Could you help me with another question?

anonymous · Answer

I asked it previously, but no one explained their answers.

mertsj · Answer

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