How to integrate with U-substitution (NancyPi)

Channel	Publish Date	Thumbnail & View Count	Download Video
	Publish Date not found	0 Views	View on YouTube Download Video

MIT grad shows how to perform integration using u-substitution (Calculus). To continue: 1) for a BASIC example where you give you exactly the expression you need to replace, go to time 1:30. 2) For an example where you need to rearrange the DU by multiplying or dividing because the du has a different number or sign than what you need, go to time 8:21. 3) For one where you need to rearrange the U by subtracting or adding because the du expression can't give you the expression you need, go to 17:15. 4) For u-substitution with TRIG (SIN/COS) and the power rule, go to 22:35. Nancy, formerly of MathBFF, explains the steps.

Follow Nancy on Instagram: https://instagram.com/nancypi
Twitter: https://twitter.com/nancypi

For my video on the FUNDAMENTALS OF INTEGRATION, go to: https://youtu.be/e1nxhJQyLYI

With all the u-substitution integration problems:

The FIRST STEP is to choose your /"u/". The best choice is usually the longer x-expression that is inside a power or a square root or the denominator, etc. (in an /"inside function/"). Equate yourself to this x-expression.

The SECOND STEP is to find /"du/" by taking the derivative of the u expression with respect to x. For example, if you have u3x2, your du would be du3dx. **NOTE: Don't forget to include /"dx/" at the end of your differential expression.

The THIRD STEP is to substitute u and du for x and dx everywhere in the integral. **NOTE: If your du doesn't perfectly match what you need to completely replace before integrating, you'll need to rearrange the du, or sometimes rearrange the u, to completely replace before integrating. For an example of each, see example #2 (time: 8:21) and example #3 (time: 5:15).

The FOURTH STEP is to integrate, remembering to add /"C/" to the end because you have integrated an indefinite integral (no limits). The du disappears when you integrate.

The FINAL STEP is to use /"back-substitute/" to replace everywhere you appear with the x-expression you chose.

For more of my math videos, visit: http://nancypi.com