Grade 12 Integral Calculus Worksheet
This worksheet covers fundamental concepts in integral calculus, including antiderivatives, definite and indefinite integrals, and applications.
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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
x³ + x² - x + C
x³ + x² - 1 + C
6x + 2 + C
x³ + 2x² - x + C
2. The area under the curve f(x) = x from x = 0 to x = 2 is:
1
2
4
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.
True
False
2. The Fundamental Theorem of Calculus links the concepts of differentiating a function and integrating a function.
True
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.