What is the Antiderivative of 5\sqrt{}x?

[jimen113]

Homework Statement

the antiderivative for 5\sqrt{}x

Homework Equations

The Attempt at a Solution

It almost looks like the derivative of the function \sqrt{}x

 

[Feldoh]

\int 5\sqrt{x} = \int 5x^{1/2}

So just use the power rule for integrals.

 

[jimen113]

revised

the actual problem is:
Evaluate the definite integral \int^{7}_{1} 5/\sqrt{}x
using the power rule I got:
5[(x^3/2)/(3/2)] evaluating them at the end points 1 and 7, the answer I get after using FTC II is:-58.400 and is incorrect.
What am I doing wrong? please help

 

[Defennder]

Do you mean \int_1^7 \frac{5}{\sqrt{x}} \ dx?

If so, then x^(3/2) shouldn't be part of your answer.

 

[jimen113]

Do you mean \int_1^7 \frac{5}{\sqrt{x}} \ dx?

If so, then x^(3/2) shouldn't be part of your answer.

Yes (to part one)
then how should I find the antiderivative? for 5/\sqrt{}x

 

[Defennder]

You must first find the antiderivate for x^{-\frac{1}{2}}. Use the power rule for integrals as Feldoh said.

 

[jimen113]

Thanks for your help!