Re: MX2 Integration Marathon
K I did that and got int(6x^3+6-(1/((x-0.5)^2+0.75)))
Final result is (3x^4)/2+6x-(2/sqrt3).tan^-1((2x-1)/sqrt3)
That right?
Re: MX2 Integration Marathon
let u^3=x, 3u^2du=dx
So integral is 3u^2/(u^3/2+u).du
take out factor of u on bottom, it cancels with one u on top so u have
3u/(sqrtu+1)
let x=sqrtu and divide 3x^2 by (x+1), get -3/3x^2 as remainder, so -1/x^2, and the rest expands to 3x^2-3
So just...
x''=0
x'=15sqrt2
x=15sqrt2t
y''=-10
y'=-10t+15sqrt2
y=-5t^2+15sqrt2t
When y=-10, t=4.67 (2dp)
so time of flight=4.67s
When t=4.67, x=99.08 (2dp), so distance travelled is 99.08m
I think thats right.