Question

Definite Integral HELP!!!

Answer 1

Correct Me If I am wrong.If not GIve Me the answer!!

Answer 2

@Fifciol @amistre64 Help

Answer 3

Is it correct??

Answer 4

you can dbl chk by taking the derivative to see if you get back to the results

Answer 5

Really need the answer!!

Answer 6

you need to develop confidence in your work too; take the derivative of what you got, does it produce the original setup?

Answer 7

Thats not my prob .My ans doesnt match with the given ans!!

Answer 8

whats the given answers, you might need to simplify it

Answer 9

Its 2(sqrt2-1)

Answer 10

I get sqrt2

Answer 11

use the identity: cosx= 2 cos^2(x/2) - 1

so the denominator becomes:

1+ 2cos^2(x/2)- 1 = 2cos^2(x/2)

and the integral is reduced to:

(1/2) ∫ sec^2(x/2) dx

Let u=(x/2) ==> du= (1/2) dx

so the integral becomes:

(1/2) ∫ sec^2(u) dx = ∫ sec^2(u) du

= tan u +c

= tan(x/2)
Then just plug in the integration limits and boom you are done!

Answer 12

csc 0 is undefined since its 1/0

1/(1+cos)

(1-cos)/sin^2

csc^2 - cotcsc

-cot + csc does seem reasonable if ive remembered my derivatives ... but then csc is still troubled, might have to take the limit

Answer 13

The formulas are a'ight ,my method isn't ,I guess!!

Answer 14

sin = 0 at 0, so we would have to take the limits of:

csc(x)-cot(x)-csc(pi/2)+cot(pi/2), as x to 0

Answer 15

But in tan(x/2) case,wont u get ans as 1??

Answer 16

the answer is 1, which is what you get when you do the limit ....

Answer 17

But give ans is 2(sqrt2-1)!!!

Answer 18

http://www.wolframalpha.com/input/?i=limit+%28x+to+0%29+csc%28pi%2F2%29-cot%28pi%2F2%29-csc%28x%29%2Bcot%28x%29

Answer 19

Must be a typo ,I guess!!

Answer 20

Thanks again!!

Answer 21

youre welcome

Answer 22

But can u tell me the ans u get by applying my method.....Pls

Answer 23

by applying your results:\[\left.csc(x)-cot(x)~\right|_{0}^{pi/2}\]since 0 is produces an undefined value for csc, we have to limit it up to zero:\[\lim_{a\to 0}\left.csc(x)-cot(x)~\right|_{a}^{pi/2}\]

Answer 24

And dat gives us??

Answer 25

1??

Answer 26

of course

Answer 27

Oh....Now I get it.Thank U very very much.Ur an awesome Helper.......!!Cheers!!

Answer 28

yw