Answer to Question #322865 in Vector Calculus for Neyoclass

Question

An example in the xy -plane. A force F=x^2yi+xy^2j acts on a body as it

moves between (0, 0) and (1, 1). Determine the work done when the path is along the line y=x.

Select one:

A. 1

B. 14

C. 13

D. 12

Answer 1

$\int_{\left( 0,0 \right)}^{\left( 1,1 \right)}{Fdl}=\left[ \begin{array}{c} y=x\\ dl=\left( dx,dx \right)\\ F=\left( x^3,x^3 \right)\\ Fdl=x^3dx+x^3dx=2x^3dx\\\end{array} \right] =\int_0^1{2x^3dx}=2\cdot \frac{1^4}{4}=0.5\\No\,\,correct\,\,variant$