Question

Calculus integration problem involving arccosx

Answer 1

\[\int\limits_{0}^{1/\sqrt{2}}arccosx/\sqrt{1-x^2} dx\]

Answer 2

im not very sure how to handle the arccosx on the top

Answer 3

put x=cos y

Answer 4

@YadielG

Answer 5

the limit turns to be
\[\int\limits_{\pi/2}^{\pi/4} (-ydy)=\int\limits_{\pi/4}^{\pi/2} ydy =(1/2) ((\pi/2)^2-(\pi/4)^2)\]

Answer 6

=
\[3\pi^2/32\]

Answer 7

hello @YadielG are you checking it?

Answer 8

i solved it

Answer 9

i did the u substitution for arccosx and it left me with \[\int\limits_{0}^{1/\sqrt{2}}-u du\]

Answer 10

then it was simple power rule and plugging in the values from there

Answer 11

the limits are wrong

Answer 12

i left them like that because i substituted x back in, I usually don't like converting the limits to fit the u form

Answer 13

ok... then you do the indefinite integral first and then convert it to x and then take the limits.. dont put the limit of x when you are doing work of u, or else its a mistake

Answer 14

yes i understand i left them off when i was showing my work but i put them here simply to restate the limits from the original problem, but anyway i appreciate the help

Answer 15

ok.. :)

Answer 16

do check that both our answers are same

Answer 17

that checks with me