Introduction to Integration
Explore the fundamental concepts of integration, including antiderivatives, indefinite and definite integrals, and their applications in finding area under a curve.
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Introduction to Integration
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Read each question carefully and provide your best answer. Show all your work for full credit.
1. Integration is the reverse process of .
2. The symbol for integration is .
3. The result of an indefinite integral always includes a of integration.
4. What is the antiderivative of f(x) = 2x?
x²
2
x² + C
2x²
5. A definite integral calculates the under a curve between two points.
slope
area
volume
perimeter
6. Find the indefinite integral of f(x) = 3x² - 4x + 5.
7. Evaluate the definite integral ∫ from 0 to 2 of (x + 1) dx.
8. The derivative of an integral is the original function.
True
False
9. A definite integral always has a constant of integration.
True
False
10. Consider the function f(x) = x + 1. Sketch this function on the graph below and shade the area under the curve from x = 0 to x = 2.
11. Based on your sketch, how does the area relate to the definite integral you calculated in question 7?