integration (1 Viewer)

[Hehe]

can someone hlep me integrate this (25-4x^2)^1/2...thanx

 

[Affinity]

1.)goto integrals.wolfram.com (or is it soemthing else)

2.)
let x = (5/2)sin(t), then dx = (5/2)cos(t) dt

so the integral

= INT ( sqrt( 25 - 25( sin(t) )^2 ) * (5/2)cos(t) dt

= 25/2 INT [cos(t)]^2 dt

= 25/4 INT [ 1 + cos(2t) ] dt

= (25/4)*[ t + (1/2)sin(2t)] + C

= (25/4)*[ arcsin(2x/5) + sin(t)cos(t) ] +C

= (25/4)*[ arcsin(2x/5) + (2x/25)*sqrt(25-4x^2) ] + C

EDIT: thanks grey, me starting to forget stuff already..

 

[Grey Council]

x/2 . (25 - 4x^2)^1/2 + 25/4 (arcsin (2x/5))

according to the integrator