# Integral Multiple Choice Problem

• Feb 22nd 2010, 02:07 PM
r2d2
Integral Multiple Choice Problem
If the Function $\displaystyle f$ is defined by f(x)= √x³ + 2 and $\displaystyle g$ is an antiderivative of f such that g (3) = 5, THEN g(1)= ??

A. -3.268
B. -1.585
C. 6.585
D. 1.732
E. 11.585

How would you go about solving this problem? thanks!
Oh and the square root sign is for both the x^3 and the 2.
• Feb 22nd 2010, 02:09 PM
Ted
Quote:

Originally Posted by r2d2
If the Function $\displaystyle f$ is defined by f(x)= √x³ + 2 and $\displaystyle g$ is an antiderivative of f such that g (3) = 5, THEN g(1)= ??

A. -3.268
B. -1.585
C. 6.585
D. 1.732
E. 11.585

How would you go about solving this problem? thanks!
Oh and the square root sign is for both the x^3 and the 2.

Well, Lets do it step by step.
You are telling that $\displaystyle g(x)=\int f(x)dx$.
Start by finding $\displaystyle g(x)$, i.e. by integrating $\displaystyle f(x)$.

What will you get?
• Feb 22nd 2010, 02:12 PM
r2d2
the integration of the x^3 +2 is where I get stuck. How would I go about doing this? u substitution?
• Feb 22nd 2010, 02:15 PM
Ted
Quote:

Originally Posted by r2d2
the integration of the x^3 +2 is where I get stuck. How would I go about doing this? u substitution?

Specify your $\displaystyle f(x)$.
In post #1 you said $\displaystyle f(x)=\sqrt{x^3}+2$ or maybe $\displaystyle f(x)=\sqrt{x^3+2}$.

And in post #3 you said $\displaystyle f(x)=x^3+2$.

Which one is your $\displaystyle f$ ?
• Feb 22nd 2010, 02:17 PM
r2d2
the square root of (x^3 + 2).

I don't know how to make a root sign that goes over both of the characters