Beginner Question on Integral Calculus

I have two questions attached, the fact that the function is f(x) but the variables are t is throwing me off.

Also, does the derivative cancel out the integral and just leave the function as is?

I appreciate any solution & quick explanation.
Calculus Functions
Janikowo Janikowo
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Matchmaticians Beginner Question on Integral Calculus File #1 File #1 (jpg)
Matchmaticians Beginner Question on Integral Calculus File #2 File #2 (jpg)
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Erdos Erdos
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  • Janikowo Janikowo
    0

    So you can just replace the t's with x's? Could you also explain how you got from the 3rd line to the 4th line in Q2?

  • Erdos Erdos
    0

    Yes. In Q2 going from 3rd line to the 4th line, note that the derivative of 2pi x^2 is 4pi x.

  • Erdos Erdos
    0

    Also sin (32 pi)=0.

The answer is accepted.
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