IGCSE/GCSE/O & A Level/IB/University Student Forum

Qualification => Subject Doubts => GCE AS & A2 Level => Math => Topic started by: houmeira on October 19, 2009, 06:18:26 pm

Title: MATHS/ Integration P3
Post by: houmeira on October 19, 2009, 06:18:26 pm: hi!
Can anyone please help to solve this question?

integral of x²e^x³ dx.

would you also show me the method. i'm trying integration by parts but im getting stuck!
Title: Re: MATHS/ Integration P3
Post by: astarmathsandphysics on October 19, 2009, 07:19:26 pm: Not integration by parts. Is integration by substitution. Sub u=x3. Will answer when i get home.
Title: Re: MATHS/ Integration P3
Post by: astarmathsandphysics on October 19, 2009, 09:17:53 pm: $\int x^2 e^{x^3} dx$
sub $u=x^3$ so $du=3x^2 dx$ so $dx=\frac {du}{3x^2}$
Integral becomes $\int x^2 e^{u} \frac {du}{3x^2} =\frac {1}{3} \int e^u du =\frac {1}{3} e^u =\frac {1}{3} e^{x^3}$
Title: Re: MATHS/ Integration P3
Post by: houmeira on October 20, 2009, 03:42:12 am: Thank you very much!!!i've got exams so thanks:))you're great!