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 ] #?

1 Answer
Jul 26, 2017

Answer:

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#