Section 5.7
Computing Definite Integrals
The Fundamental Theorem of Calculus Part 2 gives us the shortcut. We don't need infinite rectangles; we just need the Antiderivative.
1
The Subtraction Shortcut
Find the antiderivative, plug in the top, plug in the bottom, and subtract.
Fundamental Theorem Part 2
Total Change = End Height - Start Height
9 - 1 = 8.00
The red bar represents the accumulation . It matches exactly the rise in .
2
Worked Example: Polynomial
Basic Evaluation
Evaluate .
1. Antiderivative
2. Evaluate Bounds
Top (3):
Bottom (1):
3. Subtract
3
Level Up Examples
Example A: Trig Evaluation
Evaluate .
1. Antiderivative:
.2. Plug in:
.
3. Result:
.Example B: Splitting Absolute Value
Evaluate .
1. Split at V-point (0):
.2. Integrate Parts:
Part 1: .Part 2: .
3. Result:
.5
Practice Quiz
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