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Integral Calculus
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Video |
Title |
Topics |
Length |
Script |
1 |
Three ways to look at Integral Calculus |
6.5 min |
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2 |
Using the Trapezoidal Method to approximate an integral |
12.5 min |
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3 |
Using the Trapezoidal Method to approximate the integral of a function |
5.5 min |
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4 |
Informal explanation of the FTOC |
4.5 min |
||
5 |
Basic properties and review of FTOC. Typical Examples. |
9.5 min |
||
6 |
Changing the key derivatives into the key anti-derivatives. Examples. Reductive strategy for integration. |
8.5 min |
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7 |
Review of FTOC and basic properties of definite integrals. |
4.5 min |
||
8 |
Some simple integrals. Examples. Reductive strategy for integration. |
8.5 min |
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9 |
Introduction to integration by substitution. Examples. |
6.0 min |
||
10 |
Three examples.Definite integrals under substitution. |
8.0 min |
||
11 |
Two examples of substitutions of the form x = g(u) |
7.0 min |
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12 |
Three examples of integration by substitution including a definite integral |
7.0 min |
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13 |
Discussion of the importance of substitution and also an important insider tip. |
3.0 min |
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14 |
Illustration of the connection between integration and differential equations. |
7.5 min |
||
15 |
Discussion of the use of tables of integration formulas. Illustration of the method of guess and check. The importance of checking your answers |
9.0 min |
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16 |
Derivation of the Integration by Parts formula. Illustration by one example. |
6.5 min |
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17 |
Four examples of intgration by parts. |
7.0 min |
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18 |
Connection between integrals and area. |
7.0 min |
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19 |
The general area formula. Examples |
8.0 min |
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20 |
A derivation of the classical formula πr². |
13.5 min |