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MTH 174
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
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I have been working with two problems and I can't seem to find a good answer.
1. Is the antiderivative of 3t^3+4t^4-t^2 going to be 3(t^4/4)+4(t^5/5)+(t^3/3)+C or 3t^4/4 + 4t^5/5 + t^3/3 + C?
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3(t^4/4)+4(t^5/5)+(t^3/3)+C = 3t^4/4 + 4t^5/5 + t^3/3 + C. There is no difference in the two expressions except the way they are grouped.
However the correct result is
3(t^4/4)+4(t^5/5)-(t^3/3)+C, or equivalently 3t^4/4 + 4t^5/5 - t^3/3 + C
In other words you did it correctly except that you missed the - sign on the last term.
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2. Is the antiderivative of -1/t^2 going to be -x/t^2 + C?
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That would be the antiderivative of the function -1/t^2, if the integration is with respect to x.
If the integration is with respect to t, which might well be the case since t is the only variable you mention in the problem, the result would be - (-1/3 t^-3) = 1 / (3 t^3).
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I can't seem to find a definite answer.
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Check my notes and let me know if you have questions.
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