Evaluate: Essentials of Calculus integral problem

[Nawz]

Homework Statement

Evaluate:

Integral sign: Square root of 3x times dx

Homework Equations

The Attempt at a Solution

integral of 3x^1/2 dx

(3x^(3/2)) / (3/2)

so I multiplied it by 2/3 and got:

(2/3x^(3/2)) +C

but the answer is 2 times the square root of 3 divided by 3 then x^3/2.. ? I don't know how they kept the square root of 3.

 

[Mark44]

Homework Statement

Evaluate:

Integral sign: Square root of 3x times dx

I'm taking this to mean
\int \sqrt{3x}dx

The simplest way to approach this is to bring out a factor of sqrt(3), and rewriting the integral using exponents, rather than radicals.

\sqrt{3}\int x^{1/2}~dx

Can you carry out the rest of this?

Homework Equations

The Attempt at a Solution

integral of 3x^1/2 dx

(3x^(3/2)) / (3/2)

so I multiplied it by 2/3 and got:

(2/3x^(3/2)) +C

but the answer is 2 times the square root of 3 divided by 3 then x^3/2.. ? I don't know how they kept the square root of 3.

 

[Nawz]

I'm taking this to mean
\int \sqrt{3x}dx

The simplest way to approach this is to bring out a factor of sqrt(3), and rewriting the integral using exponents, rather than radicals.

\sqrt{3}\int x^{1/2}~dx

Can you carry out the rest of this?

Wow. Yes that makes it much easier. When can you do this? Can you do it For all constants in front of an x? Is it recommended to do that?

 

[Mark44]

Yes, you can always move a constant into or out of an integral.