Question

Question #92bd2

Answer 1

• Differentiation gives you the rate of change of the function.

For example:

1. Velocity (v) is rate of change of displacement (x)
   So, `v = dx/dt`
2. Acceleration (a) is rate of change of velocity (v)
   So, `a = (dx)/dt`

• When you integrate, you are finding the signed area under the curve

For example work done is Area under curve fromed in Force vs displacement graph

Finding Work done by a variable force

`dW = F.dx`

`W = int(3x^2 + 2x - 10)dx`

`W = (cancel(3)x^3)/cancel(3) + (cancel(2)x^2)/cancel(2) - 10x + c`

`W = x^3 + x^2 - 10x + c`