A particles moves along x - axis from x = 0 to x = 7m under the influence of a force given by `f(x)=12-2x+3x^(2)` then the workdone is,

Options

A. 205 J
B. 390 J
C. 378 J
D. 291 J

Answer

C

Explanation

Workdone dw = Fds
`w=int_(0)^(7)F.ds = int_(0)^(7)(12-2x+3x^(2))dx`
`=[12-(cancel(2)x^(2))/(cancel(2))+(cancel(3)x^(3))/(cancel(3))]_(0)^(7)=12(7-0)-(7^(2)-0)+(7^(3)-0)`
`=84-49+343 = 378 J`