Query Assignment 5

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11:16:56 query 5.1.12 integrate t^4 dt and check by differentiation

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RESPONSE --> I have the antiderivative as t^5 / 5 + c. The derivative of 1/5 t^5 is 1/5 * 5 t^4 = t^4

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11:19:04 ** An antiderivative of this power function is one power higher so you will have a multiple of t^5. Since the derivative of t^5 is 5 t^4 an antiderivative will be t^5 / 5. Adding the arbitrary integration constant we end up with general antiderivative t^5 / 5 + c. The derivative of 1/5 t^5 is 1/5 * 5 t^4 = t^4), verifying our antiderivative. **

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RESPONSE --> ok i understand

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11:21:46 query 5.1.18 integrate v^-.5 dv and check by differentiation

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RESPONSE --> The derivative of 2 v^(1/2) is 2 * (1/2) v^(-1/2) = v^(-1/2)

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11:23:51 ** An antiderivative of this power function is a constant multiple of the power function which is one power higher. The power of the present function is -.5 or -1/2; one power higher is +.5 or 1/2. So you will have a multiple of v^.5. Since the derivative of v^.5 is .5 v^-.5 an antiderivative will be v^.5 / .5 = v^(1/2) / (1/2) = 2 v^(1/2). Adding the arbitrary integration constant we end up with general antiderivative 2 v^(1/2) + c. The derivative of 2 v^(1/2) is 2 * (1/2) v^(-1/2) = v^(-1/2), verifying our antiderivative. **

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RESPONSE --> ok i understand

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11:24:58 Query Add comments on any surprises or insights you experienced as a result of this assignment.

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RESPONSE --> i don't have any at this moment"

Good work. Let me know if you have questions.