Ask Questions, Get Answers

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

Prove the following\[\int\limits_0^1x\;e^x\;dx=1\]

Can you answer this question?

1 Answer

0 votes
  • (i)$\int \limits_a^bf(x)dx=F(b)-F(a)$
  • (ii)$ \int udv=uv-\int vdu$
  • (iii)$ \int e^x dx=e^x dx$
Given $I=\int\limits_0^1x\;e^x\;dx=1$
Clearly this is of the form $ \int udv=uv-\int vdu$
Let $u=x$ on differentiating w.r.t x we get, $du=dx$
Let $dv=e^x.dx4$ on integrating we get,$v=e^x$
Now substituting for u,v,du and dv we get,
$I=\int\limits_0^4x\;e^x\;dx=(xe^x)_0^1-\int _0^1 e^x.dx$
On integrating we get,
on applying the limits we get
But $ e^0=1$
Therefore $1e^1-e^1+1$
Therefore I=1.
Hence proved


answered Feb 19, 2013 by meena.p
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