Answer to Question #322865 in Vector Calculus for Neyoclass

Question #322865

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


1
Expert's answer
2022-04-06T11:44:50-0400

"\\int_{\\left( 0,0 \\right)}^{\\left( 1,1 \\right)}{Fdl}=\\left[ \\begin{array}{c}\ty=x\\\\\tdl=\\left( dx,dx \\right)\\\\\tF=\\left( x^3,x^3 \\right)\\\\\tFdl=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"


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