Integral Calculus Worksheet
Practice problems for integral calculus, covering basic integration, definite integrals, and applications.
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Integral Calculus Practice
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Read each question carefully and show all your work. Simplify your answers where possible.
1. Find the indefinite integral of the following functions:
a) ∫ (3x² + 2x - 5) dx
b) ∫ (4√x + 1/x²) dx
2. Evaluate the following definite integrals:
a) ∫ from 0 to 2 of (x³ - 2x) dx
b) ∫ from 1 to 4 of (1/√x) dx
3. If F(x) = ∫ from 0 to x of (t² + 1) dt, what is F'(x)?
2x
x² + 1
(x³/3) + x
x² + 1 + C
4. Find the area under the curve y = x² + 1 from x = 0 to x = 3.
5. Complete the following statements regarding properties of integrals:
a) ∫ from a to b of f(x) dx + ∫ from b to c of f(x) dx =
b) ∫ from a to a of f(x) dx =