Wednesday

August 20, 2014

August 20, 2014

Posted by **kathryn** on Tuesday, August 25, 2009 at 7:52pm.

i did the p- integral theorem with 1/square root of x and got it to be a divergent integral. however i was told this was the wrong way and that i should do it by integration by parts. but i can't figure it out by that method. please help. thanks.

- calculus -
**Count Iblis**, Tuesday, August 25, 2009 at 9:07pmYou can proceed as follows. Substitute:

x = e^t. Then the integral becomes:

Integral from ln(2) to infinity of

e^(t/2)/t dt

We can get rid of the factor 2 in the exponential by putting y = t/2. The integral becomes:

Integral from 1/2 ln(2) to infinity of

e^(y)/y dy

For positive y we have

e^(y) > 1

It follows from this that the integral is larger than

Integral from 1/2 ln(2) to infinity of

1/y dy

but this is already divergent, so the integral diverges.

**Related Questions**

Calculus - Find the exact area of the region enclosed by the square root of (x...

Algebra - Use the quadratic formula to solve the equation. Give exact answers: ...

calculus - how do you determine the convergence of : definite integral from 1--&...

Calculus AB (AP) - Hi, I have a calculus test tomorrow and I understand how to ...

calculus - is this correct? use the integral test to determine if this series is...

Maths Calculus Derivative Integral - Urgent Please - Use 2nd Fundamental Theorem...

Math simplifying mixed radicals - Please help me simplify these following mixed ...

Algebra - Rationalize each expression by building perfect nth root factors for ...

Pre Algebra - Please help me with some problems. Thank you! Solve the equation ...

Math ~CHECK MY ANSWER~ - 1) Which of these is a rational number? a. Pi b. Square...