Question

The force applied against a moving object travelling on a linear path is given by `F(x)= sinx + 1`. How much work would it take to move the object over `x in [ 0, (5pi) / 2 ]`?

Answer 1

I got `8.85J`

Explanation:

Here the force depends upon the displacement `x` so we need to evaluate the Work in integral form.
We have that:

`dW=F(x)dx` that represents a very small (infinitesimal) work.

To find the complete Work we integrate to get:

`W=int_0^(5pi/2)F(x)dx=int_0^(5pi/2)[sin(x)+1]dx=-cos(x)+x|_0^(5pi/2)=`

We use the Fundamental Theorem of Calculus and get:

`=[-cos(5pi/2)+5pi/2]-[-cos(0)+0]=0+5pi/2+1-0=5/2(3.14)+1=8.85J`