Trigonometric Integrals Powers of Sine and Cosine Calculus 2 BC 5 Examples

Examples using Guidelines A and B at 5:04 , 9:07 and 12:28
Example involving Power-Reducing Identity at 15:45
Example Involving Power Reducing Identity and Integration by Parts at 21:45

Trigonometric Integrals Powers of Tangent and Secant

Integration by Parts 6 Examples LIATE

[georgesadler]

Professor RobBob, thank you for a solid explanation and analysis of Trigonometric Integrals Powers of Sine and Cosine in Calculus Two BC. In all five examples, multiple equal signs are missing between the problem and the solution. Please correct these errors in the video.

[iccedlemontea]

Amazing explanation, makes the work much easier to break down after watching your video! Thank you so much and keep up the awesome content!!

[TooMuchTigerero]

Great video. You should consider covering series and sequences! You would explain it so well!

[profrobbob]

New #calculus  lesson Trigonometric Integrals Involving Powers of Sine and Cosine.

[dazzlembungele]

This has been very helpful for me Prof Bob and I also like the way you enter by jumping.

[HERKFOOT]

This is one of the hardest parts to Calculus 2, that's what my teacher said and i can see why! I'm still following your videos mr tarrou! Luckily this current summer semester class will finally be my last math class! (only other one is a lower one, stats) Thanks again for all the video help!

[aashsyed]

well yo explained very very nicely :)
hope you reach millions faster
very underrated :)

[howardlam]

15:45 you can also use the euler identity sin x = (exp (ix) - exp(-ix))/2i first then apply binomial theorem at the expansion and integrate each exponential function with the binomial cofficient easily. The same thing can be applied to fractional power. This is applied to obtain the fourier transform of the centred difference "Grunwald" like Riesz derivative.

[JazminZenteno]

I have a question on example 2, if it's just sin (x) instead of sin (2×) would it be 1/1 instead of 1/2?

[shrooqalhazmi]

thank you so much .. your videos always save my life

[williamma]

When I can not read my professor's handwriting or when my notes do not make sense when he doesn't change his corrections or when he's going 100mph on that blackboard I end up here to look for clues. I find it amazing how you are able to cover the same amount of material in about the same amount of time as my professor without rushing through everything.

[mannyx]

For example 4: why did you change cos(4x) to cos(8x)?

[isabel]

I have a question on example 4 at the last step before you take the integral of cos(4x). Why did you take the 4 out before i.e (4(cos(4x)) instead of putting it as (sin(4x)) since we are taking the integral of it?

[Zzznmop]

hmm for the example at 21:45, would it be wrong to do integration by parts from the first step? for example let u=x, du=dx and dv=INTEGRALcos^2(x)dx and *using power reducing identity to get v* v=INTEGRAL(1/2)cos(2x)+(1/2). So now when we substitute everything into (u*v - (INTEGRAL) v du), vdu easily integrated. clean it up with algebra and done.

[sean_tristan]

In example 4, what if the angle is odd? Say, sin^4(3x)? Does it become cos(3x) after using the Power Reducing Formulas?

[ecuador]

Your videos have been very helpful all the way to mexico, thank you very much and keep doing what you know best

[chyrickjaypontillas]

sir bob, i am wondering about the derivative of cos2x = isn't NEGATIVE how about the negative sign?

[nebuwacharles]

BAM!!!, Thanks a lot Mr. Tarrou, this is what we are being taught right now in the class. I really found it helpful.

[nesuburak]

hI I'm from Morocco i love your videos, thank you very much and keep doing what you know best (y)

[TheKirkster]

10:18 how did you learn to write so fast!