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Posted: **March 30th, 2012, 4:51 pm**

Evaluating Definite Integrals

The Integral of a Constant
If f(x) = c, where c is a constant, on the interval [a, b], then
$\int_{a}^{b}f(x)dx=\int_{a}^{b}cdx =c(b-a)$

example:
$\int_{-3}^{7}edx=$ e(7 – (–3)) = 10e

Posted: **April 16th, 2012, 11:07 pm**

Rules for Definite Integrals

1. Order of Integration

$\int_{b}^{a}f(x)dx=-\int_{a}^{b}f(x)dx$

$\int_{a}^{b}f(x)dx=-\int_{b}^{a}f(x)dx$

2. Zero Rule

$\int_{a}^{a}f(x)dx=0$

3. Constant Multiple

$\int_{a}^{b}kf(x)dx=k\int_{a}^{b}kf(x)$

4. Sum and Difference

$\int_{a}^{b}[f(x)+g(x)]dx=\int_{a}^{b}f(x)dx+\int_{a}^{b}g(x)dx$

5. Additivity

$\int_{a}^{c}f(x)dx-\int_{a}^{b}f(x)dx=\int_{b}^{c}f(x)dx$

Fundamental Theorem of Calculus
Part 1: for DERIVATIVES
f(b)b' – f(a)a'

Part 2: for INTEGRALS
F(b) – F(a)

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