Find area of y = f(x) between a ≤ x ≤ b
b
● Shortened: ∫ f(x)dx
a
Examples
3
● ∫ 2x −
1
2 dx
○ You can either take the area after graphing it out, or take the antiderivative
(integral) directly
○ x
2 − 2x
■ The antiderivative
○ (3)2 − 2(3) = 3
■ Plug in b for x
○ (1)2 − 2(1) = − 1
■ Plug in a for x
○ (3) − (− 1) = 4
■ Subtract a from b to find the area between the two points
The Integral using limit definition
b
● ∫ f(x)dx = lim
n
∑ f(xk
)Δx
a
n→∞ k = 1
n
● ∑ 1 = n
k=1
●
n
n
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