Question

check my ans please... integrate x^2/sqroot (4-x^2) dx

Answer 1

Not quite right. You have to remember sin(2x)=2sin(x)cos(x) But you know sin(x)=x/2 and cos(x)=sqrt(4-x^2)/2 Plug those in. In other words, sin(2x)=/= just x

Answer 2

Also, the integral of -cos(2x) is (1/2)(-sin(x)) there is no sign change there. Your integral should be:
2arcsin(x/2)-(1/2)xsqrt(4-x^2)+C

Answer 3

Keeping the - and replacing sin(x) and cos(x)

Answer 4

mm..wait

Answer 5

my integral is 4sin^2 tetha dtetha

Answer 6

i linealized

Answer 7

Okay, good.

Answer 8

and i got 1/2(1-cos(2tetha)

Answer 9

=1/2-1/2cos(2tetha) dtetha

Answer 10

taking the integral separately i have

Answer 11

1/2tetha + 1/4sin(2tetha)

Answer 12

So you have:
\[4/2 \int\limits 1-\cos(2\theta)d \theta=2\theta-\sin(2\theta)+C=2\theta-2\sin(\theta)\cos(\theta)+C\]
Then you have expressions for sin(theta) and cos(theta)

Answer 13

wait

Answer 14

derivative of cos

Answer 15

ohhhhhhhhhhh

Answer 16

got u i tood teh derivative

Answer 17

got it

Answer 18

And you know that x=2sin(theta) and that sqrt(4-x^2)=2cos(theta)
Solving and plugging back in you get what I have above^^

Answer 19

:))))..lol

Answer 20

so i got 2arcsine(x/2) - x sqroot (x^2-4) + c

Answer 21

In front of the sqrt there should be a (1/2) because you have 2sin(theta)=x which replaces 1/2 the expression but you have (sqrt(4-x^2))/2=cos(theta)

Answer 22

So there is a (1/2) there

Answer 23

ayyyy ..

Answer 24

oh

Answer 25

so should be 1/2x sqroot (x^2-4)

Answer 26

Yes :)

Answer 27

omgggg this test smell like something is burning,, :(

Answer 28

Haha, its okay :P

Answer 29

can u check my other qs. some anser but i feel insecure do

Answer 30

Of course :P