Calculus 2: Trigonometric Substitution (Video #3)

Examples applying trigonometric substitution in order to evaluate indefinite and definite integrals. Three cases explained with multiple examples; uses of the Pythagorean identities, additional integration techniques, and nuanced mathematical skills. #trigonometricsubstitution #trigintegrals #trigsubstitution #integrals #integralcalculus #calculus2 #mathtvwithprofessorv #calculusvideos #calculus2videos #integralvideos #trigonometricintegrals #math #youtubemath #mathvideos #mathtutor #mathprofessor #calculusvideos

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Professor V

Calculus 2 Lecture Videos on Integration:

Trig Review:

Calculus 3 Video Lectures:

#mathwithprofessorv #integration #partialfractions #partialfractionmethod #partialfractiondecomposition #trigonometricsubstitution #trigintegrals #trigsubstitution #integrals #integralcalculus #calculus2 #calculusvideos #calculus2videos #integralvideos #trigonometricintegrals #math #youtubemath #mathvideos #mathtutor #mathprofessor #calculusvideos #integrationbyparts #integralcalculus

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[acmfamily]

Thank you so much for this video! You’ve made the incomprehensible much easier!

[acmfamily]

Also, thank you for the thought, “I’m an advanced Calculus student, I can handle this.”

[_Queen_burrito_]

your videos are so easy to understand! the color coding helps alot! thank you

[AlienAura]

how are you solving for theta? you said tan(theta)=1 and got theta=pi/4 x_x

[Mikebigmike]

brilliant video, love the colour coding what are you doing these problems on? is it a large iPad or? thank you in advance

[energent]

On 30:28 why did we use case 1 instead of case 2 because I thought that the addition of a^2 + x^2 would mean using tan(theta)?

[elizabethrogers]

I have a question, at 10:39 shouldn't the radical be divided by 5?

[angelinaibay]

At 22:20, If the radical involved Subtratcing 13 instead of adding 13, would we be using case 1?

[marohe]

that simplifying in example #4. it just kept goingggg

[tlhokmokoena]

At 33:15 you said the antiderivative of tan theta is ln sec x but is it not ln cos x

[evertheking]

THANK YOU FOR MAKING THIS EASY TO UNDERSTAND

[angusriffraff]

At the start of the video you said that trig sub is for radicals with a sum or diff of squares. The given integrand in Example 4 doesn't have a radical. How is use of trig sub justified for this problem?

[funwatchtv]

I am having a bit of trouble with the examples that have completing the square, do you by any chance have a video explaining it.

[abdiabdirahman]

The algebra is the hardest part. keeping track of the negative, doing the perfect square the right way, making sure the fractions you combine are right keeps my heads spinning. The calc isn't so bad especially with professor V making these amazing videos

[juliekrasnick]

This is so helpful thank you! Why do you take out a factor of tan and sec (around 17:43 in the video)? What rule applies here?