Work of a Line integral correction please

[Bibhatsu]

Homework Statement

Compute the Work of the following line integrals in the vector field $$\vec{V}=(2x^{2}-3y;4xy;3x^{2}z)$$

Homework Equations

For the following lines:

Curve1: $$\vec{r}(a)=(a,a,a^{2}); \ 0\le a \le 1$$

Curve2: $$\vec{r}(a)=(a,a^{2},a); \ 0\le a \le 1$$

The Attempt at a Solution

For the first Curve I got $$\frac{7}{6}$$ and for the second one $$\frac{121}{60}$$.

Is this correct?Thank you in advance

Bibhatsu

 

[CompuChip]

I did the calculation quickly, but I got 3/2 for the first one.
Can you maybe show a little more work?

 

[SammyS]

I did the calculation quickly, but I got 3/2 for the first one.

I got 3/2 also.

 

[Bibhatsu]

Hey guys, so the second one is correct ? This is the integral I figured for the first one:

$$\int _{0}^{1} -3a+2a^{2}+4a^{3}+6a^{5}da=\frac{7}{6}$$Edit: there should be an integral symbol in front of the $$_{0}^{1}$$, seems it won't render. Sorry! Thanks for your feedbackBibhatsu

 

[SammyS]

4xy = 4a² when x=a and y=a.

The integral should be:

$$\int _{0}^{1} -3a+2a^{2}+4a^{2}+6a^{5}\,da$$

(To see the result of editing a Latex expression, press the Browser's reload icon after pressing the Preview Changes button.)

 

[Bibhatsu]

Hello,I see my mistake.Thank you. Greetings

Bibhatsu

 

[Bibhatsu]

Hello,


I see my mistake.


Thank you.


Greetings

Bibhatsu