Question

Need some help with this calculus question?

Answer 1

It's this:

Answer 2

I've integrated it to get: \[y =\sin 2 \theta \]

Answer 3

is this right, now can I put the limits onto it, being that theta is 0 and pie/4

Answer 4

y=(sin2θ)/2

Answer 5

Is that it at the integrated stage?

Answer 6

if so could you explain how you came by that answer please?

Answer 7

Overall I got y= [0.0137060668 as my final answer.

Answer 8

Take the derivative of his function, you will see that it gives the cosine of 2θ. One formal way to get this is by u-substitution (substitute u for 2θ and du=2dx so du/2 for dx, then integrate)

Answer 9

I'm still confused.

Answer 10

the derivative of
\[\sin(2\theta)\] is
\[2\cos(2\theta)\] by the chain rule
so \(\sin(\theta)\) is not the anti derivative of \(\cos(2\theta)\)

the anti derivative of \(\cos(2\theta)\) is \(\frac{1}{2}\sin(2\theta)\)

Answer 11

Just use u substitution if you're unsure
\[\Large \int\limits_{0}^{\pi/4} \cos 2 \theta d \theta\] let \[ \large u = 2 \theta\] Try it this way.

Answer 12

Could you do an example of u substitution please?

Answer 13

Try this http://archives.math.utk.edu/visual.calculus/4/substitutions.3/

This first one may be helpful http://archives.math.utk.edu/visual.calculus/4/substitutions.3/int1.html

Answer 14

I'll take a look

Answer 15

y = sin2theta / 2 that's what I got.

Answer 16

That's it.

Answer 17

Ok, so now, With this the limits can be applied to the theta, which is 0 and pie/4.

y = [ sin2theta / 2 ]^pie/4 - [ sin2theta / 2 ]^0

y = [ sin2(pie/4) / 2 ] - [ sin2(0) / 2 ]

y = [ sin2(0.7853981634) / 2 ] - [ sin2(0) / 2 ]

y = [ sin(1.570796327) / 2 ] - [ sin2(0) / 2 ]

y = [ 0.02741213359 / 2 ] - [ sin(0) / 2 ]

y= [ 0.0137060668 ] - [0 ]

y = 0.0137060668

y = 0.013

Answer 18

Your calculator is probably in degrees, those are radians.

Answer 19

https://www.google.com/search?q=sin(2*0.7853981634)%2F2&aq=f&oq=sin(2*0.7853981634)%2F2&aqs=chrome.0.57j0.674j0&sourceid=chrome&ie=UTF-8

Answer 20

Yes it was I degrees. I got y= 0.5 overall as my final answer.

Answer 21

*in