Integral with sqrt(a^2-x^2) -- inverse trig function needed

See midnighttutor.com for the latest calculus tutorial videos. Tutorial of how to solve integrals involving this construct which require inverse trig functions to solve.

Category:

Howto & Style

Tags:

• calculus
• integral
• integration
• inverse
• trig
• tutorial

[gnatz182]

This video is excellent, wonderfully explained.

To those people who say that just by looking at it you can tell that it's arcsin, yes, that is true, but knowing it as a recognition rule and not a solid derivation is useless.

[icafemoto]

NEVERMIND, i think i figured it out myself.

After solving for C, -arccos(x) + C = arcsin(x)

C = pi/2

[yingmujielun]

so what if a is not equal to 1?

[saad095]

if it was possible to integrate this equation without using da substitution method then one could have got the value of pi by integrating this circle equation between 1 and -1 Hell pi and e always create a fuss

[dsilvestre]

Isn't Sqrt(1-sin^2(t)) = |cos(t)| ?

(Observe the absolute value)

I don't understand why he simply says it equales cos(t)

(It's in the middle of the whiteboard)