# Can't seem to integrate this rectilinear motion equation.

Hi, so I have a question where it asks me to find the distance between t = 0 and t = 60 for the equation v = 1/6(t(60 - t)). First I had to find the values of t which the object moving was stationary, that was simple enough. (It's been around a month and a half since I did rectilinear motion). It then asks me to to find the distance between t = 0 and t = 60. I'm having somewhat trouble simplifying the equation ready for integrating. This is my try at it:

v = 1/60(t(60 - t))
v = t - t2/60

After this, I'm stuck, it's been too long since I've done any real maths... I'm not sure, all I need is an equation without fractions so it's easy enough to integrate.

Do you know how to integrate the first part?
The integral of t (with respect to t)
add 1 to the power, divide by the new power.

For the second part, the part that includes the fraction, this fraction (-1/60) is just a constant. So, integrate t^2 then simply place the constant (-1/60) in front of it.
Remember, to integrate t^2 (with respect to t), you simply add 1 to the power (here the power is 2) then divide by the new power.

Then combine the answers of the 2 integrals (t and -1/60 t^2) and don't forget to add the constant of integration.

e.g. the integral of t^3/2 is (t^4/4)/2=t^4/8+constant.

Oh god, of course. I never did do many integratation including fraction, thanks for clearing that up for me though. So whenever you integrate a variable with a coefficient what a fraction, you simply integrate the variable and switch the fraction around and multiply it. Thanks a lot!