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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Includes

Multiple ChoiceFill in the Blanks2 Short AnswerTrue / False

Standards

CCSS.MATH.CONTENT.HSF.IF.B.4CCSS.MATH.CONTENT.HSF.IF.C.7e

Topics

CalculusIntegralsAntiderivativesGrade 12Math

7 sections · Free to use · Printable

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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 + 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.