need help finding the definite integral

Question

el_arrow · Answer

$$\int\limits_{-1}^{0.4} y \sqrt(1-y^2) dy$$

el_arrow · Answer

i got the -1 which is -pi/2 but how do i do the 0.4

el_arrow · Answer

y=sin(theta)

el_arrow · Answer

@satellite73 how do i do it?

anonymous · Answer

what did you get for the anti derivative? you can plug in the numbers

anonymous · Answer

oooh i see, did you use a trig sub?

el_arrow · Answer

yeah that what im using for this problem

anonymous · Answer

too much work
use $u=1-x^2$ and you get it almost in your head

anonymous · Answer

$$-\frac{1}{2}\int_0^{.84}\sqrt{u}du$$

el_arrow · Answer

wait how did you get that 0 and .84

el_arrow · Answer

your plugging them in for x?

anonymous · Answer

unless you want to substitute back might as well change the limits of integration when you do the u - sub

anonymous · Answer

$$u=1-x^2,u(-1)=0,u(.4)=.84$$

el_arrow · Answer

oh okay

el_arrow · Answer

but i am using trig identities

el_arrow · Answer

whats the sin of .84? lol

el_arrow · Answer

like i got the integral using trig substitution

anonymous · Answer

?

el_arrow · Answer

not u-substitution

anonymous · Answer

then substitute back 
it is too much work but if you want it may work
what did you do?

anonymous · Answer

$$x=\sin(\theta), dx=\cos(\theta)d\theta$$ 
$$\int \sin(\theta)\cos^2(\theta)d\theta$$

anonymous · Answer

you don't want the sine, you want the arcsine

el_arrow · Answer

yeah thats what i meant

anonymous · Answer

you still have to do a u - sub at this point, so why not do one u-sub instead of two?

el_arrow · Answer

cause its too easy

anonymous · Answer

lol enjoy
as for arcsine, use a calculator

el_arrow · Answer

okay thanks

anonymous · Answer

yw

el_arrow · Answer

your right u-substitution was easier

el_arrow · Answer

i got u=y^2 and du=2y