Question

evaluate the integral (√(1/x)-2) dx from 1 to 4

Answer 1

is the -2 in the square root or not ?

Answer 2

it is not

Answer 3

sorry, i have to go now. let me tag my best friends :)
@ganeshie8 , @whpalmer4

Answer 4

So is that\[\int_1^4 (\sqrt{\frac{1}{x}} -2) dx\]

Answer 5

thanks :)

Answer 6

yes

Answer 7

Well, we can split this into two integrals:

\[\int_1^4 \sqrt{\frac{1}{x}}\,dx - \int_1^4 2\,dx \]right? Can you tell me the result for the right-hand integral?

Answer 8

The left hand integral you can rewrite if you recall that \[\large \sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}\]and \[\large \sqrt{x} = x^{\frac{1}{2}}\]

Answer 9

That gives you an expression to which you can apply the power rule for integration.