# Math Help - Integral help

1. ## Integral help

Im having trouble solving these intergrals...if anyone can help thatd be great,
Compute the integral from -1 to 3 of the square root of (6-2x^2+4x) dx..

Also, evaluate the indefinate integral of dx / square root of (1-x^2+2x)

I know where to start, but i keep getting stuck where i have to take the antiderivative of ax^-1..which would be x^0 which doesnt make sence...

2. Originally Posted by shmayer
Im having trouble solving these intergrals...if anyone can help thatd be great,
Compute the integral from -1 to 3 of the square root of (6-2x^2+4x) dx..

Also, evaluate the indefinate integral of dx / square root of (1-x^2+2x)

I know where to start, but i keep getting stuck where i have to take the antiderivative of ax^-1..which would be x^0 which doesnt make sence...
$\int \sqrt{6-2x^2+4x} \, dx$

$\int \sqrt{8 - 2(x^2 - 2x + 1)} \, dx$

$\int \sqrt{8 - 2(x-1)^2} \, dx$

now use the trig substitution $x-1 = 2\sin{t}$

$\int \frac{1}{\sqrt{1-x^2+2x}} \, dx$

$\int \frac{1}{\sqrt{2 - (x^2-2x+1)}} \, dx$

$\int \frac{1}{\sqrt{2 - (x-1)^2}} \, dx$

you should recognize this integral form's antiderivative as an arcsine function.