MATH PROF vs TRICKY INTEGRALS

In this video we are going to try three tricky integrals using standard first year calculus integration techniques like integration by parts, partial fractions, trig substitution and conjugates, but each is a little bit disguised. Do I still remember how to do these???

0:00 Double Integration by Parts
5:02 Get Maple Calculator for step-by-step solutions
7:12 u-subs and integration by parts
12:13 conjugate, trig sub, integration by parts

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[stevehof]

This is a perfect refresher before returning to work in the Math Assistance Centre this semester! Thanks Trefor!

[johnchessant]

For integrating sqrt(x^2-1), it might be easier to do x = cosh(t), so then sqrt(x^2-1) dx = sinh(t)^2 dt which we can expand in terms of exp(t). Then we do the integral and convert back using exp(t) = exp(arccosh(x)) = x + sqrt(x^2-1).

[theedspage]

It can be easy to miss the negative signs and other simple errors when we are focused on the integral.

[oliviab]

Trefor, every time you post I feel like I just get to relax and hang out with you - what a positive environment you cultivate! I guess, as a Math major, I'm your specialized audience, but I recommend everyone I know your videos whenever I get the chance. Thank you for your content.

[HDitzzDH]

11:05 There should be a negative sign in front of the first term since the derivative of (1-u) is -1.

[aashsyed]

The first integral can also be solved by letting u=sinx. Then the double integration by parts is much easier to think about.

[douglasstrother]

Integration with Dr. Bazett is *way* more fun than it was when I had 20 problems like this as an undergrad!

In hindsight, plotting the integrand, and playing around with integration by parts, partial fractions, trig substitutions, etc. without the pressure of "getting it right the first time" would have made learning integrals much easier. Calculus is very geometric, so learning how to draw pictures helps enormously with developing an intuition to approaching problems.

[johnsalkeld]

Generally i like to note that 1/(1-A) (1+A) = 1/2(1/(1-A) + 1/(1+A)) and apply this with first A = u^2 then A = u which can be done by writing out the general form and stating the application.

[gunhasirac]

Nice practices for integration techniques. One little comment on the partial fraction part: if you notice the expression is product of 2 degree 2 polynomials that are missing the x’s, you can eyeball it by two steps, first into 2 deg 2 polynomial terms then final result.

[legendarynoob]

For the second integral you write tan in terms of sine and cosine and use double angle formula for cosine.
Then you'll end up with (1+cos(2x))/2cos(2x) inside the integral. The nice thing is there is no need for partial :) fractions if you do things this way :) .

[abdulmoiz]

sir you are amazing. I got A grade in my calculus exams just because of your videos. Thanks.

[bensay]

So awesome! Haven’t seen integrals this tough since learning integration, so this is a great refresher. Thank you!

[sanketbhangale]

At 11:11 Sir you should also divide the term by the coefficient of u as it is a linear expression

[nileshchakraborty]

Great videos, make more videos about integral calculus. Love from India.

[budokan]

I've never seen an integration problem as a fun puzzle, it's just a boring chore a routine work a tedious task to solve with a computer. The real fun may be to learn how to program these machines for this purpose.

[nurjafri]

Reminds me so much of my early interaction with integrals :'). I always wanted to dive deep, never got a chance ;/

[thedarkknight]

Integrating partial fraction is way easy👍
Enjoyed the video :)
Can you make a video similarly on Walli's formula?

[gabj]

Amazing video, I love your work. I believe A = C = -1/4 and B = D = 1/4 (I ended up there a couple of times)

[morischacter]

Ughh for the first integral, I picked u as arcsin^2x then changed my dv to arcsinx, and then gpt zero. I guess you always have to be consistent with your u and dv right?

[intereststcentury]

Remember those dr I used to love them (and still)!!! U never fail to explain those in an epic way. So I would like to ask you if you are going to upload a Probability and Statistics course for this fall. Thank You Dr amd God Bless 🙏