course Mth 174
I'm getting very comfuse on section 7.1. I pict #11 to try to figur out. can you show me how to use substution on #11 for section 7.1.end of document
Remember that you have to give me the details of the problem and tell me what you do an do not understand about the situation.
I happen to be at the same place my book is, so I can address this problem. However it would still be very good if I knew what you were thinking about it, what you have tried, etc..
The integrand is t^2 ( t^3 - 3)^10.
You could try u = t^2, or u = t^3, or u = t^3 - 3.
If you try u = t^2, then du = 2 t dt and that doesn't get you anywhere.
If you try u = t^3, then du = 3 t^2 dt; the expression t^2 ( t^3 - 3)^10 dt does contain t^2 dt as a factor. Since 3 t^2 dt = du, we have t^2 dt = 1/3 du, so the expression could be written (u - 3)^10 * (1/3 du) = 1/3 (u - 3)^10 du. This expression is fairly easy to integrate, but the third alternative choice of u is even better.
If you try u = t^3 - 3, then again du = 3 t^2 dt. Now expression t^2 ( t^3 - 3)^10 dt can be written as just u^10 * (du / 3) = 1/3 u^10 du.
The antiderivative is thus 1/3 ( u^11 / 11) + c = 1/3 (t^3 - 3)^11 / 11 + c = 1/33 ( t^3 - 3)^11 + c.
Let me know if this helps. The idea is to try every possible choice of u, looking for a choice in which the expression for du is a factor of the expression you are trying to integrate.