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!