Definite integrals : 2 problems

: 131.151 Calculus 1 for Engineers: Definite integrals : 2 problems
   By Ariel B on Sunday, December 04, 2005 - 03:13 pm: Edit Post

Hello professor Sasho:
while studying deinite integral i got confused with two things:
1) there we did in class the definite integral between -5 and 5 of the absolute value of X, we divided then the integral into 2 smaller parts: from -5 to 0 and from 0 to 5. is this method only apply for absolute values?

2) While doing one of the questions from past final exams i got to the point where i had to find the integral between 0 and 1 of (xe^x)^2
i tried different ways of solving it but im not sure how to approach this problem.(i was thinking about (xe^2x) but im not sure if thats the right approach),

thank you very much for your time,
Ariel B.


   By Sasho on Sunday, December 04, 2005 - 04:18 pm: Edit Post

1, That method relies on a property we have stated in class and that property applies in general and so it could be applied to other functions too. We did it in that particular case because it helped us deal with the absolute value.

2. My guess is that you have made an error at some point. The function you give is x2e2x and evaluating the integral of that function requires "integration by parts", a method that we have not covered in this course.


   By Ariel B on Sunday, December 04, 2005 - 06:16 pm: Edit Post

Professor Sasho:
thanks a lot for the quick answer.
about the second part i found this question on the final exam from December 12,2000 page 8.

the questions states:
the definite integral between 0 and 1 of:
(sin 2x + (xe^x)^2) dx
i started the question by separating it into two smaller integrals. I did solve it for sin 2x but the problem is in the next part.

once again, thank you very much for your time


   By Sasho on Sunday, December 04, 2005 - 06:37 pm: Edit Post

Are you sure it is not xex2, rather then (xex)2? Otherwise, perhaps 151 in 2000 covered integration by parts. In any case the question as you have stated it does not seem suitable for what we have covered in this course, this year.


   By Ariel B on Sunday, December 04, 2005 - 07:07 pm: Edit Post

it is exactly the first case you mentioned(the one with no brackets). So in that case i should not worry about that kind of question on the exam?

thanks,


   By Sasho on Sunday, December 04, 2005 - 07:19 pm: Edit Post

Yes.


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