integral from 0 to 1 of cos(arcsinx)

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integral from 0 to 1 of cos(arcsinx)

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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Let \[\theta =\sin^{-1} x\]
Therefore \[x/1=\sin \theta =opp/hyp\]Draw my triangle x is opp, 1 hyp, sq rt (1-x^2) adj
From that triangle you have info to find cos theta which you would integrate

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Other answers:

do you integrate cos theta or cos (sqrt(1-x^2)) ?
cos theta in and of itself does not contain the info in your problem. However cos theta (which essentially is your problem) is equal to sq root (1-x^2) which contains all relevant info. So integrate sq rt (1-x^2).
how do you integrate sq rt(1-x^2)?
You have to find relevant trig sub.
Your instructor gives very interesting problems. What school? what course?
University of Miami: Calculus II
Go 'Canes
Lol! Thanks

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