Question

The force applied against a moving object travelling on a linear path is given by `F(x)=3x^2+x`. How much work would it take to move the object over `x in [2,3 ]`?

Answer 1

21.5 J

Explanation:

work done = `f*dx`
here F=`3*x^2+x`
substituting and integrating from 2 to 3 we get
W=`int_2^3(3x^2+x).dx`
w=`[x^3+x^2/2]_2^3`
`[27+9/2]-[8+4/2]`
`19+5/2`
`43/2`=`21.5J`