Introduction to Integrals
This worksheet introduces Grade 11 students to the basic concepts and applications of integrals in calculus, covering indefinite and definite integrals.
Includes
Standards
Topics
Introduction to Integrals
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Date:
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Read each question carefully and provide the best answer. Show all your work for full credit.
1. Integration is the reverse process of .
2. The symbol ∫ represents the .
3. The constant of integration, denoted by , is added to indefinite integrals.
4. What is the antiderivative of f(x) = 2x?
x²
x² + C
2
2x²
5. A definite integral represents the under a curve.
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 (2x + 1) dx.
8. The Fundamental Theorem of Calculus relates differentiation and integration.
True
False
9. The area under the curve y = x from x=0 to x=1 is 1.
True
False
10. A particle moves along a straight line with a velocity function v(t) = 3t² - 6t. Find the displacement of the particle from t=0 to t=3.
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