Problem in calculating work done?

[navneet9431]

Homework Statement

See question number 3

Homework Equations

Work Done="integral" F*ds

The Attempt at a Solution

I tried to solve this question using integration,

I have replaced F with "1" and ds with "t^2+2t".
So I am stuck in at that step.
Please help me differentiate it further or solve it further!
I will be thankful for any help!

 

[jedishrfu]

In the integral it’s $F*ds$ which becomes $F*dx$ so you can’t just sub in the $t^2+2t$ term.

$dx/dt = 2t+2$ and so $dx = (2t+2)dt$

 

[navneet9431]

In the integral it’s $F*ds$ which becomes $F*dx$ so you can’t just sub in the $t^2+2t$ term.

$dx/dt = 2t+2$ and so $dx = (2t+2)dt$

Thanks for the reply!
But can you please explain why is it wrong to substitute "t^2+2t" in place of ds?

 

[haruspex]

Thanks for the reply!
But can you please explain why is it wrong to substitute "t^2+2t" in place of ds?

You are not given ds (or dx)= t²+2t; you are given x=t²+2t. So what does dx equal?