Grade 12 Calculus: Introduction to Integrals
This worksheet covers fundamental concepts of integrals, including antiderivatives, definite and indefinite integrals, and their applications.
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Grade 12 Calculus: Introduction to Integrals
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Read each question carefully and provide detailed answers. Show all your work for full credit.
1. What is the antiderivative of f(x) = 3x²?
x³
x³ + C
6x
6x + C
2. The definite integral ∫ from 0 to 1 of x dx represents:
The slope of the tangent line at x=1
The area under the curve y=x from x=0 to x=1
The volume of a solid of revolution
The instantaneous rate of change of x
3. The process of finding the antiderivative is called .
4. The Fundamental Theorem of Calculus links differentiation with .
5. Find the indefinite integral of f(x) = 4x³ - 2x + 5.
6. Evaluate the definite integral ∫ from 1 to 2 of (3x² + 1) dx.
7. The constant of integration, C, is only added for definite integrals.
True
False
8. If F'(x) = f(x), then ∫ f(x) dx = F(x) + C.
True
False
9. The velocity of a particle is given by v(t) = 6t² - 4t. Find the displacement of the particle from t=0 to t=2.
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