Ask Questions, Get Answers

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

Evaluate the definite integrals\[\int\limits_0^1\frac{dx}{\sqrt{1+x}-\sqrt x}\]

Can you answer this question?

1 Answer

0 votes
  • (i)$\int \limits_a^bf(x)dx=F(b)-F(a)+c$
  • $\int x^n dx=[\frac{x^{n+1}}{n+1}]+c$
Given $I=\int\limits_0^1\frac{dx}{\sqrt{1+x}-\sqrt x}$
Let us multiply and divide by its conjujate,
Therefore $I=\int\limits_0^1\frac{dx}{\sqrt{1+x}-\sqrt x} \times \frac{\sqrt {1+x}+\sqrt x}{\sqrt {1+x}+\sqrt x}$
$=\int\limits_0^1\frac{\sqrt {1+x}+\sqrt x}{1+x-x}dx$
$=\int\limits_0^1({\sqrt {1+x}+\sqrt x})dx$
On seperating the terms,
$I=\int\limits_0^1\sqrt {1+x}dx+\int \limits_0^1\sqrt x\;dx$
On integrating we get,
On applying limits,
$=\frac{2}{3} \bigg\{2^{3/2}-1+1 \bigg\}+c$



answered Feb 19, 2013 by meena.p

Related questions

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