# Math Help - Definite integral of parametric equation

1. ## Definite integral of parametric equation

$

\int^1_{-1} {(4ti+2t^3j-\sqrt[3]{t}k)} dt

$

Sadly, I'm supposed to tutor someone in calculus III tomorrow and am going through the homework tonight and came across this. No idea how to solve whatsoever. Can someone point me in the right direction?

Thank in advance.

2. Originally Posted by Negativ
$

\int^1_{-1} {(4ti+2t^3j-\sqrt[3]{t}k)} dt

$

Sadly, I'm supposed to tutor someone in calculus III tomorrow and am going through the homework tonight and came across this. No idea how to solve whatsoever. Can someone point me in the right direction?

Thank in advance.
are $i=e_1=(1,0,0)$ etc?

3. Yes, they are unit vectors. 1,0,0 ; 0,1,0 ; 0,0,1

4. Originally Posted by Negativ
Yes, they are unit vectors. 1,0,0 ; 0,1,0 ; 0,0,1
What's the problem then? We integrate a vector valued function coordinate-wise.

5. Meaning that I integrate them all separately? (And if so, I don't understand how to integrate the last piece since I don't know what $-1^{4/3}$ is.

6. Still unclear on this. Any help appreciated.

7. Originally Posted by Negativ
$

\int^1_{-1} {(4ti+2t^3j-\sqrt[3]{t}k)} dt

$

Sadly, I'm supposed to tutor someone in calculus III tomorrow and am going through the homework tonight and came across this. No idea how to solve whatsoever. Can someone point me in the right direction?

Thank in advance.
$\int^1_{-1} {(4t\vec{i}+2t^3\vec{j}-\sqrt[3]{t}\vec{k})}= \left(\int_{-1}^1 4t dt
\right)\vec{i}+ \left(\int_{-1}^1 2t^3 dt\right)\vec{j}- \left(\int_{-1}^1 t^{1/3} dt\right)\vec{k}$

8. First two are zero, unsure on last one is what I was unclear on. Sorry for not being specific.

9. Originally Posted by Negativ
First two are zero, unsure on last one is what I was unclear on. Sorry for not being specific.
It is 0 as well.

Since $t^{\frac{1}{3}}$ is symetric