Definite Integral Practice
This worksheet provides practice problems on evaluating definite integrals, understanding their properties, and applying them to calculate areas.
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Definite Integral Practice
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Read each question carefully and show all your work. Simplify your answers where possible.
1. Evaluate the definite integral: ∫ from 0 to 2 of (3x^2 - 4x + 1) dx
2. Evaluate the definite integral: ∫ from 1 to 3 of (1/x) dx
3. Given that ∫ from 1 to 5 of f(x) dx = 7 and ∫ from 3 to 5 of f(x) dx = 4, find ∫ from 1 to 3 of f(x) dx.
3
11
-3
4
4. Find the area of the region bounded by the graph of y = x^2, the x-axis, and the vertical lines x = 0 and x = 3.
5. The Fundamental Theorem of Calculus Part 1 states that if F(x) = ∫ from a to x of f(t) dt, then F'(x) = .
6. The Fundamental Theorem of Calculus Part 2 states that ∫ from a to b of f(x) dx = F(b) - F(a), where F is any of f(x).
7. The definite integral of a function represents the area under the curve only if the function is non-negative over the interval.
True
False
8. If ∫ from a to b of f(x) dx = 0, then f(x) must be 0 for all x in [a, b].
True
False