Integral Calculus> integrate the following integral ∫ 1 / sq...

integrate the following integral
∫ 1 / sqrt(x + a) + sqrt(x + b) dx

taniska , 11 Years ago

Grade 12

1 Answers

Jitender Singh

Last Activity: 11 Years ago

Ans:
Hello Student,
Please find answer to your question below

$I = \int \frac{1}{\sqrt{x+a}+\sqrt{x+b}}dx$
$I = \int \frac{\sqrt{x+a}-\sqrt{x+b}}{(\sqrt{x+a}+\sqrt{x+b})(\sqrt{x+a}-\sqrt{x+b})}dx$
$I = \int \frac{\sqrt{x+a}-\sqrt{x+b}}{a-b}dx$
$I = \frac{1}{a-b}[\int \sqrt{x+a}dx-\int \sqrt{x+b}dx]$
$I = \frac{1}{a-b}[\frac{2(x+a)^{3/2}}{3}-\int \sqrt{x+b}dx]$
$I = \frac{1}{a-b}[\frac{2(x+a)^{3/2}}{3}-\frac{2(x+b)^{3/2}}{3}]+c$
$I = \frac{2}{3(a-b)}[(x+a)^{3/2}-(x+b)^{3/2}]+c$