How Do You Integrate Work with a Changing Angle Theta?

[morssolis]

here is the problem. w= f*d*cos(theta). theta is changing so it involves integration.

i know the answer its about 52. i know one solution for it but i have been trying to figure out how to solve it integrating with respect to theta. the way i know to solve it is let

cos(theta)= x / ((x^2)+(h^2))^(-1/2), then integrate this with respect to x with a u substitution.



i thought that the integral from theta at x1 to theta at x2 of F*d*cos(x) dtheta would work, however it does not. i have been trying to figure this out for days.

any ideas how you can solve this by integrating with theta as opposed to x?

Thanks

 

[ehild]

$$W=\int_{x1}^{x2}{F \cos{\theta} dx}$$

It is easy to integrate by substituting u=x^2+h^2.

ehild

 

[morssolis]

well thank you for the input however i know that already. i said that in the OP. i am trying to figure out how to integrate with respect to theta

 

[ehild]

F=T is constant. Substitute x / ((x^2)+(h^2))^(-1/2) for cos(theta) in the integral and calculate it.

ehild