integrating inverse tan/sine/cos

[n.]

how do you integrate inverse sine/cos/tan?

[taiga]

Integration by parts, you don't need to know how to do it in spesh

[n.]

really? its in my textbook-essential maths

[xZero]

you mean arcsin arccos and arctan?

[n.]

arent they the same thing?

[sajib_mostofa]

So they tell you in your book to integrate expressions such as  ? If thats the case, don't worry about it as someone mentioned. Not examinable at VCE level.

[Mao]

It's not too much of a stretch from VCE materials. (Since they are one-to-one functions)

1. Pick a point on the y=arcsin(x) graph (any point)
2. Draw straight lines to the x and y axis from that point. You now make a rectangular box.
3. The area enclosed by y=arcsin(x) and the y axis can be found by integration (hint: x=sin(y), definite integral)
4. The area enclosed by y=arcsin(x) and the x axis is thus the area of rectangular box subtract the above integral. This is the integral of arcsin(x)

[pi]

Integration by parts, you don't need to know how to do it in spesh

+1, we did it in class. Not in the course though, but still interesting to know

[n.]

ill probably just do it anyway

thanks for all you help 

[jimmy999]

You kind of do need to know how to do these. Just look at the VCAA 2008 exam 1, last question I believe.

Obviously you'll do it by Mao's method where you don't directly integrate it, but you find the solution by integrating it along the y axis and subtracting from areas etc.

[golden]

You kind of do need to know how to do these. Just look at the VCAA 2008 exam 1, last question I believe.

Obviously you'll do it by Mao's method where you don't directly integrate it, but you find the solution by integrating it along the y axis and subtracting from areas etc.

Hmm maybe it is quite important then...

By the way nice SS for Specialist Mathematics.