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How to take integral

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Matthew Manzer

Definite integral of rational function (video)

Let’s take a final look at the following integral. ∫ 2 0 x2+1dx ∫ 0 2 x 2 + 1 d x Both of the following are anti-derivatives of the integrand. F (x) = 1 3 x3 +x and F (x) = 1 3x3 +x − 18 31 F ( x) = 1 3 x 3 + x and F ( x) = 1 3 x 3 + x − 18

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Definite Integrals

1. Understand the notation for integration. An integral ∫abf(x)dx{\displaystyle \in2. Understand the definition of an integral. When we talk about integrals, we usu3. Remember See more
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Calculus 1 : How to find integral expressions

Using the Rules of Integration we find that ∫2x dx = x2 + C. Now calculate that at 1, and 2: At x=1: ∫ 2x dx = 12 + C. At x=2: ∫ 2x dx = 22 + C. Subtract: (2 2 + C) − (1 2 + C) 2 2 + C − 1 2 − C. 4 − 1 + C − C = 3. And C gets cancelled out so with
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