Ask Questions, Get Answers

Want to ask us a question? Click here
Browse Questions
Home  >>  CBSE XII  >>  Math  >>  Integrals
0 votes

Integrate the function\[x^2e^x\]

Can you answer this question?

1 Answer

0 votes
  • (i)Let us consider two functions u and v and if they are of the form $\int u dv,$then we can solve it by the method of integration by parts\[\int udv=uv-\int vdu\]
  • (ii)$\int e^xdx=e^x+c.$
Given $I=\int x^2e^x dx.$
Clearly the given integral function is of the form $\int u dv$,so let us follow the method of integration by parts where \[\int udv=uv-\int vdu\]
Let $u=x^2$.
On differentiating we get
Let $dv=e^xdx.$
On integrating on both sides we get
On substituting for u,v,du and dx we get,
$\int x^2e^xdx=(x^2.e^x)-\int e^x.2xdx.$
$\;\;\;=(x^3e^x)-2\int e^x.xdx.$-----(1)
Again $\int e^xdx $ is of the form $\int u dv.$
Let u=x.
On differentiating we get
let $dv=e^xdx.$
On integrating we get
Hence on substituting for u,v,du and dv we get
$\int x.e^xdx=(xe^x)-\int e^xdx.$
On integrating we get
Substituting this in equ(1) we get
$\int x^2e^xdx=x^2e^x-2(xe^x-e^x)+c.$
Taking $e^x$ as the common factor we get


answered Feb 8, 2013 by sreemathi.v
Ask Question
student study plans
JEE MAIN, CBSE, NEET Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App