Integration by Substitution: Definite Integrals

Calculus: We note how integration by substitution works with definite integrals using the First Fundamental Theorem of Calculus. Two methods are given, and examples used are (a) int_0^1 x(x^2+1)^5 dx, (b) int_0^{pi/4} tan(x) sec^2(x) dx, (c) int_{-1}^1 x(1-x^2)^2 dx, and (d) int_0^2 x(1-x^2)^2 dx.

[MathDoctorBob]

@ruigatinho You're welcome, and thanks for the kind words! Please let me know if you have any specific requests. - Bob

[helenamelon]

Thank you! That was very clear and precise, I appreciate it.

[MathDoctorBob]

You're welcome! Thanks for the kind words. - Bob

[nreddy]

Great vid. keep up the good work mate!

[DarktitanX]

very helpful and easy to understand, thanks you

[RedRainDrop]

you scared the shite out of me. your a hulk of a man. very nice tutorials.
could you make more difficult examples?

[MathDoctorBob]

@DarktitanX2 You're welcome! - Bob

[MathDoctorBob]

@pomijanlewa You're welcome! Good luck with exams. - Bob

[MathDoctorBob]

Thanks! As Popeye said, I yam what I yam. :) Check the calculus playlist at the mathdoctorbob website. I have about five more examples videos on substitution. If that's not enough, let me know what you have in mind. - Bob