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State the Fundamental Theorem of Calculus Part 2.
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The definite integral of a function f from a to b equals F(b) - F(a), where F is the antiderivative of f.
In Example 2, what is the result of finding the definite integral of 5x - 4 from 1 to 4?
The result is 51/2 or 25.5.
What does the integral sign (∫) represent?
The integral sign represents a limit of sums in an integral.
How is the integral of the square root of x from 4 to 9 calculated?
Convert sqrt(x) to x^(1/2), apply the power rule, and evaluate F(9) - F(4) to get the result of 2.
What is the value of the definite integral from 1 to e of 5/x dx in Example 4?
The value is 5.
Explain the difference between indefinite and definite integrals.
Indefinite integrals do not have upper and lower limits, resulting in a function plus a constant of integration. Definite integrals have upper and lower limits, resulting in a specific numerical value.
How is the integral of 8x^{-3} from -3 to 4 evaluated?
Rewrite x^{-3} properly to use the power rule, find the antiderivative, simplify, and evaluate F(4) - F(-3) to get the result of 7/36.
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