Question

a variable force of F (x) =4x^2 applied on body calculate the workdone in a moving the body from x=2m to x=3m​

Answer 1

Given : a variable force of F (x) =4x^2 applied on body

To Find :  the work done in a moving the body from x=2m to x=3m​

Solution:

F (x) =4x²

dW  =  Fdx

=> dW  =  4x²dx

Integrating both sides

=> ∫dW  = ∫ 4x²dx

work done in a moving the body from x=2m to x=3m​

$\int dW =\int\limits^3_2 {4x^{2} } \, dx$

$W = \left {\dfrac{4x^{3}}{3} } \right ]_2^3$

$W = {\dfrac{4\times 3^{3}}{3} } - {\dfrac{4\times2^{3}}{3} }$

W = 36 - 32/3

W = 76/3

Work done is 76/3  joule

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Answer 2

Step-by-step explanation:

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