Most of the thanks goes to my wife who does the bulk of the work filming, editing, producing, and uploading the videos as well as making the thumbnails. 🙂
Timestamp 4:27 How do we know that the halfway point (pi/4) coincides with the intersection of the two functions? Any reference videos please? Again, great video as always!
@@MichelvanBiezen Wow thank you for your response! I was posed this as a challenge question in my class and was trying to devise a way that would allow me to do a single integral but maybe manipulate the functions to allow me to compensate for the functions switching positions. A negative coefficient did not work. Thank you again for the response. I definitely will drop a like and check out your other videos
Since the the graph between 0-π/4 and π/4-π/2 are mirror image so can't we just 2x integration of [sin x] with limit being 0-π/4 ? would that be correct ?
The expression 0 < x < 2 pi indeed means that you have to integrate from 0 to 2 pi. You have to find all the points where the functions cross over and integrate each section separately (and make sure you have the correct y1 - y2 or y2 - y1 setup for each section).
Best Calculus video of the year!
The red bow tie makes calculus so much more bearable
Mamasaurus Rex so true!!! I like calculus anyways but his bow tie stands out from the other videos
A lifesaver, thank you so much for all your time and effort into creating these resources!
Most of the thanks goes to my wife who does the bulk of the work filming, editing, producing, and uploading the videos as well as making the thumbnails. 🙂
@MichelvanBiezen Tell her she does an amazing job and that we all thank you guys very much
I will make sure to tell her. 🙂
Levi, Thank you! - Zong
Timestamp 4:27 How do we know that the halfway point (pi/4) coincides with the intersection of the two functions? Any reference videos please? Again, great video as always!
At 45 degrees (pi/4) the value of the sin and cos are equal (sqrt(2) / 2 = 0.707....)
@@MichelvanBiezen oh I remember that from the previous videos. Thank you!
Really well made video. Very clear and helped a ton. Thanks.
Thank you, these certain examples with flipped orders are rare in TH-cam for some reason.
lovely... it made things clearer
Helped me with my presentation in school. Although I had to do it in German because... obvious reasons. But excellent video.
Wow ! Love from india❤
Thank you. Welcome to the channel.
Thank you so much, Professor!
You're very welcome!
bruh since when do y=sinx and y=cosx intersect and the x axis
Is there any way to find the area by integrating as a single integral? Is there a way to keep the limits of integration from 0 to pi/2 ?
Since the 2 functions switch positions (in the vertical direction) I would not recommend it.
@@MichelvanBiezen Wow thank you for your response! I was posed this as a challenge question in my class and was trying to devise a way that would allow me to do a single integral but maybe manipulate the functions to allow me to compensate for the functions switching positions. A negative coefficient did not work. Thank you again for the response. I definitely will drop a like and check out your other videos
Thank you, you just earned another subscriber!
Since the the graph between 0-π/4 and π/4-π/2 are mirror image so can't we just 2x integration of [sin x] with limit being 0-π/4 ? would that be correct ?
Try it both ways and see if you get the same answer.
find the area to sin x and x axis between bay /2 to x = 2 pay
Helpful Sir🖤
Glad to hear that
@@MichelvanBiezen 😍
Big help, thank you
If Y2=SinX and Y1=Cosx Graph of SinX is not Correct.
Take a look at the video, the functions are correct. We left of the arrows pointing to the graph on the thumbnail.
thank you
Grt sir
Why on y axis and not on x axis
thanks
Great video, it really helped me out
how to proove that is really (pai/4)
set sin(x) = cos(x) and solve for x. sin = cos only when angle = 45 degrees (theta = pi/4)
Sir i cannot catch up anything😭 i have similar question like this but its 0
The expression 0 < x < 2 pi indeed means that you have to integrate from 0 to 2 pi. You have to find all the points where the functions cross over and integrate each section separately (and make sure you have the correct y1 - y2 or y2 - y1 setup for each section).
Thanks Sir!
Most welcome!
too good
(x^2)d^2y/dx^2 -dy/dx -4x^3y =8x^3 sinx^2 ,x>0
Please help
I love you