course mth 272 ÉÄ°\Ï÷Ÿ†öí¼Ã|èçr»z”ïÐassignment #005 005. `query 5 Applied Calculus II 06-29-2008
......!!!!!!!!...................................
07:46:35 5.1.12 integrate 3 t^4 dt and check by differentiation
......!!!!!!!!...................................
RESPONSE --> you want to use the constant multiple rule here. =3 integral sign t^4dx =3(t^5/5) + C = (3/5)t^5 +C confidence assessment: 2
.................................................
......!!!!!!!!...................................
07:48:39 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. **
......!!!!!!!!...................................
RESPONSE --> ok i forgot to check with differentiation. the derivative of 3/5 t^5 is 3/5 * 5 t^4 = 3 t^4) self critique assessment: 2
.................................................
......!!!!!!!!...................................
07:53:09 5.1.20 (was 5.1.18) integrate v^-.5 dv and check by differentiation
......!!!!!!!!...................................
RESPONSE --> = integral sign v^.5/(.5) + C = (1/2)v^.5 + C confidence assessment: 2
.................................................
......!!!!!!!!...................................
07:56:56 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. **
......!!!!!!!!...................................
RESPONSE --> ok i see where I slightly messed up. it should be 2 instead of (1/2) when you move it up from the denominator. Again the the derivative of 2 v^(1/2) = 2* (1/2) v^(-1/2) = v^(-1/2) verifying the antiderivative self critique assessment: 2
.................................................
......!!!!!!!!...................................
08:00:33 Add comments on any surprises or insights you experienced as a result of this assignment.
......!!!!!!!!...................................
RESPONSE --> the only thing was that I thought when you have v^(1/2) / (1/2) + C = 1/2v^(1/2) but it should be 2v^(1/2) could you explain why this is so please? confidence assessment: 3
.................................................