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- What can you say about integrals over adjacent intervals?
- How do you take the integral of a function over an interval?
- What are the rules for definite integrals?
What can you say about integrals over adjacent intervals?
The additive interval property says we can break up integrals into pieces (integrals on smaller intervals with the same integrand). Specifically, the integral over the interval [a,c] is the same as the sum of the integrals over [a,b] and [b,c] when a≤b≤c.
How do you take the integral of a function over an interval?
If a function f(x) is defined in the interval (a,c) then ∫caf(x)dx ∫ a c f ( x ) d x can be calculated by adding the definite integral of the function over adjacent intervals: ∫caf(x)dx=∫baf(x)dx+∫cbf(x)dx ∫ a c f ( x ) d x = ∫ a b f ( x ) d x + ∫ b c f ( x ) d x .
What are the rules for definite integrals?
Rule: Properties of the Definite Integral
The integral of a sum is the sum of the integrals. The integral of a difference is the difference of the integrals. for constant c . The integral of the product of a constant and a function is equal to the constant multiplied by the integral of the function.
