Question

a particle moves along the y axis from x=0 to x=5 under the influence of a Force given by 7-2x+3x³.find the work done in this process

Answer 1

for variable force
workdone (w) = F (x).dx

now,
W=F (x).dx
=(7-2x+3x^3) .dx
=7.dx -2.xdx +3 x^3.dx
=7[x] -[x^2]+ 3/4 [x^4]

now put limit x=5 to x=0
W =7 [5-0] -[5^2-0] +3/4 [5^4]
=35-25+3/4 x 625
=10 + 1875/4
=10 + 468.75
=478.75 joule