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7:30 12:39 Suggested clip Integration By Tables — YouTubeYouTubeStart of suggested client of suggested clip Integration By Tables — YouTube
0:12 2:27 Suggested clip How to use a Table of Integrals — Part 1 — YouTubeYouTubeStart of suggested client of suggested clip How to use a Table of Integrals — Part 1 — YouTube
0:09 8:18 Suggested clip 5.2.3 — Estimating definite integrals from tables — YouTubeYouTubeStart of suggested client of suggested clip 5.2.3 — Estimating definite integrals from tables — YouTube
Standard Integrals. (cos x) DX = sin x + C where C is the constant of integration discussed earlier. Based on this principle we present a list of common integration formulae useful in integrating any given function. If a function to be integrated is in any of the above forms, then we directly use the formula.
A symbolic integration utility consists, in part, of a database of integration tables. The primary difference between using a symbolic integration utility and using a table of integrals is that with a symbolic integration utility the computer searches through the database to find a fit.
Integral ex. Ex DX = ex + C.
A “S” shaped symbol is used to mean the integral of, and DX is written at the end of the terms to be integrated, meaning “with respect to x”. This is the same “DX” that appears in Dy/DX. To integrate a term, increase its power by 1 and divide by this figure.
Declare a variable u and substitute it into the integral: Differentiate u = 4x + 1 and isolate the x term. This gives you the differential, Du = 4dx. Substitute Du/4 for DX in the integral: Evaluate the integral: Substitute back 4x + 1 for u:
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