what is the integral of sin arccosin x?

Answer 1

Well, first of all sin(arccos x) = sqrt(1-x²). My table of integrals says integral ( sqrt(a²-u²)) = u/2 • sqrt(a²-u²) + a²/2 • arcsin(u/a) + C.

So replacing u with x and a with 1, we get x/2 • sqrt( 1-x²) + 1/2 • arcsin(x).

And my TI-89 agrees.

Answer 2

Since Cosec^-1(x) = sinx
Reason put Cosec^-1(x)= t
1/cosec x =t
sin x = t
therefore
sin arccosin = sin(sinx)
put sin x = t then on differentiation cos x dx =dt
sqrt(1- sin^2(x)) dx =dt
sqrt(1- t^2) dx =dt
dx =[1/(sqrt(1- t^2))] dt
and now complete the integration by parts your self

Answer 3

sin arccosine x=sin arcsine (pi/2-x)
which is pi/2-x which on integration gives
pi/2x-x^2/2+C

Answer 4

Saint arccosin x?

Answer 5

There isn't one.

However, the integral of sinx is -cosx and the integral of arccosx is xarchcosx - root(x-1)root(x+1) o_o

Answer 6

if you mean ∫sin(arc cos(x)) so i can help you;

∫sin(arc cos(x)) = 1/2 ( (√1 - x^2) + arc sin(x) )

Good Luck.