Question

When a particle is located a distance x feet from the orgin, a force of x^2+2x punds acts on it. How much work is done in moving it from x=1 to x=3

Answer 1

the equation for work in one dimension is \[W=\int\limits_{1}^{3}F dx\] and F is given as F=x^2+2x, so our equation becomes\[W=\int\limits_{1}^{3}(x ^{2}+2x) dx=\left[ x ^{3}/3 +x ^{2} \right]\] from x=1 to x=3 \[(3^3/3+3^2)-(1^3/3+1^2)=9+9-1/3-1=50/3\]