7.1 Exercise 32

A particle moves along a curved path $y \left(x\right) = \left(10 \text{m}\right) \left\{1 + \text{cos} \left[\left(0.1 \left( \text{m}\right)^{−1}\right) x\right]\right\} ,$ from $x = 0$ to $x = 10 \pi \text{m},$ subject to a tangential force of variable magnitude $F \left(x\right) = \left(10 \text{N}\right) \text{sin} \left[\left(0.1 \left( \text{m}\right)^{−1}\right) x\right] .$ How much work does the force do? (Hint: Consult a table of integrals or use a numerical integration program.)