course Mth 272

¥½Þäàe¡”´»r½ëÔY“¾ÏlĤÁØ‹záúassignment #005

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005. `query 5

Applied Calculus II

07-24-2007

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13:58:05

5.1.12 integrate 3 t^4 dt and check by differentiation

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RESPONSE -->

the answer is ((3t^5) / 5) + C

confidence assessment: 3

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13:58:14

An antiderivative of the power function t^4 is one power higher so it will be a multiple of t^5. Since the derivative of t^5 is 5 t^4 an antiderivative of t^4 is be t^5 / 5. By the constant rule the antiderivative of 3 t^4 is therefore 3 * t^5 / 5. Adding the arbitrary integration constant we end up with general antiderivative3 t^5 / 5 + c.

The derivative of 3/5 t^5 is 3/5 * 5 t^4 = 3 t^4), verifying our antiderivative. **

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RESPONSE -->

got it

self critique assessment: 3

You don't appear to have checked your result by differentiation.

.

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13:58:53

5.1.20 (was 5.1.18) integrate v^-.5 dv and check by differentiation

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RESPONSE -->

the anser is...

2v^(1/2) + C

confidence assessment: 3

You don't appear to have checked your result by differentiation.

.

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13:59:04

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 -->

self critique assessment:

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13:59:09

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

self critique assessment: 3

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13:59:22

Add comments on any surprises or insights you experienced as a result of this assignment.

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RESPONSE -->

I think I understand it all

confidence assessment: 3

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"

Good, but be sure you always check integration results by differentiation.