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Grade 12 Integral Calculus Worksheet

This worksheet covers fundamental concepts in integral calculus, including antiderivatives, definite and indefinite integrals, and applications.

Grade 12 Math CalculusIntegral Calculus
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Includes

Fill in the BlanksMultiple Choice2 Short AnswerTrue / False

Standards

CCSS.MATH.CONTENT.HS.C.A.1CCSS.MATH.CONTENT.HS.C.A.2

Topics

CalculusIntegralsAntiderivativesDefinite IntegralIndefinite Integral
7 sections · Free to use · Printable
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Grade 12 Integral Calculus Worksheet

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Read each question carefully and show all your work. Simplify your answers where possible.

1. The process of finding the antiderivative is called  .

2. If F'(x) = f(x), then F(x) is an   of f(x).

3. The integral from a to b of f(x) dx is called a   integral.

1. Evaluate ∫ (3x² + 2x - 1) dx

a

x³ + x² - x + C

b

x³ + x² - 1 + C

c

6x + 2 + C

d

x³ + 2x² - x + C

2. The area under the curve f(x) = x from x = 0 to x = 2 is:

a

1

b

2

c

4

d

0

1. Find the indefinite integral of f(x) = 4x³ - 6x² + 5.

2. Evaluate the definite integral ∫ from 1 to 3 of (2x + 1) dx.

1. The power rule for integration states that ∫ xⁿ dx = (xⁿ⁺¹)/(n+1) + C, for any real number n.

T

True

F

False

2. The Fundamental Theorem of Calculus links the concepts of differentiating a function and integrating a function.

T

True

F

False

The velocity of a particle moving along a straight line is given by v(t) = 3t² - 6t m/s. Find the total distance traveled by the particle from t = 0 to t = 3 seconds.