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
Name:
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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