SOLUTION: Evaluate the integral the integral of the product of the quantity x times the square root of 1 minus x, dx. negative x squared over 3 times the quantity 1 minus x raised to the

Algebra ->  Finance -> SOLUTION: Evaluate the integral the integral of the product of the quantity x times the square root of 1 minus x, dx. negative x squared over 3 times the quantity 1 minus x raised to the      Log On


   



Question 1025369: Evaluate the integral the integral of the product of the quantity x times the square root of 1 minus x, dx.
negative x squared over 3 times the quantity 1 minus x raised to the three-halves power, plus C
x squared over 3 times the quantity 1 minus x raised to the three-halves power, plus C
the quotient of the quantity 2 minus 3 times x and 2 times the square root of the quantity 1 minus x, plus C
negative 2 divided by 15 times the quantities 2 plus 3 times x and the quantity 1 minus x raised to the three halves power, plus C

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
int%28x%2Asqrt%281-x%29%2Cdx%29
.
.
.
Integrate by parts,
int%28v%2Cdu%29=uv-int%28u%2Cdv%29
.
.
du=%281-x%29%5E%281%2F2%29dx
v=x
So then,
u=int%28%281-x%29%5E%281%2F2%29%2Cdx%29=-%282%2F3%29%281-x%29%5E%283%2F2%29
dv=dx
and
uv=-%282%2F3%29x%281-x%29%5E%283%2F2%29

Putting it all together,


int%28x%2Asqrt%281-x%29%2Cdx%29=%281%2F15%29%281-x%29%5E%283%2F2%29%28-10x-4%281-x%29%29
int%28x%2Asqrt%281-x%29%2Cdx%29=%281%2F15%29%281-x%29%5E%283%2F2%29%28-10x-4%2B4x%29
int%28x%2Asqrt%281-x%29%2Cdx%29=%281%2F15%29%281-x%29%5E%283%2F2%29%28-6x-4%29
int%28x%2Asqrt%281-x%29%2Cdx%29=-%282%2F15%29%281-x%29%5E%283%2F2%29%283x%2B2%29