Question

Find integral from 0 to 1/sqrt2 of arccosx/(1+x^2)^1/2.

Answer 1

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

Answer 2

this is the work they have. but what i don't get is how they got the 1/2

Answer 3

are u there this is simple to solve...

Answer 4

when u see the derivative of the function in your integral then u just use the simple porwer rule

Answer 5

so in ur case u have the derivative of arccosx in the denominator, hence, all u have to do is use 1/2 arcsin^2(x). recall the basic 1/n+1x^(n+1)

Answer 6

also notice the arc cosx became arc sinx

Answer 7

so u can use the u sub

Answer 8

one of the ways to solve this problem or refer to the table

Answer 9

the 1/2 should be there try the u sub. u'll see u'll get 1/2 u^2

Answer 10

oh wait. i think i see what your saying @mathsmind
cuz it's basically just integral u du right?

Answer 11

i will show u in details

Answer 12

no, no, i understand
thanks :)

Answer 13

oh ok yes u got what i said

Answer 14

so keep that in mind and remeber it like ur name

Answer 15

-_- what?

Answer 16

it is very important to search for the derivative in an integral before u solve it

Answer 17

i mean remeber the concept that we just said like ur name

Answer 18

that will help u solve integrals in ur mind

Answer 19

i never saw the answer u posted because i don't open image files

Answer 20

what do integrals have to do with my name?

Answer 21

this is a metaphor i meant that remeber this rule like u know ur name, the same way if someone ask u about ur name, for example if one ask u what is ur name, you know the answer straight way, so know this rule in the same manner...

Answer 22

ohhh ok. sorry. i'm slow
thanks for your tip :)