Question

A variable force of 6x−2 pounds moves an object along a straight line when it is x feet from the origin. Calculate the work done in moving the object from x = 1 ft to x = 15 ft. (Round your answer to two decimal places.)

Answer 1

Answer:

644 J

Step-by-step explanation:

F = 6x -2

x1 = 1 ft , x2 = 15 ft

Let dW be the small amount of work done in moving with a small distance dx.

dW = F dx

Now integrate both sides within proper limits

$\int dW = \int_{1}^{15}(6x -2)dx$

$W =[3x^{2}-2x]_{1}^{15}$

W = (3 x 225 - 2 x 15) - (3 - 2)

W = 644 J