Definite Integral Worksheet
A Grade 9 math worksheet focusing on the concept and calculation of definite integrals.
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Definite Integral Worksheet
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Read each question carefully and provide your answer in the space provided. Show all your work for full credit.
1. In your own words, explain what a definite integral represents geometrically.
2. The definite integral of a function f(x) from a to b is denoted by ∫ f(x) dx, where 'a' is the lower limit and 'b' is the limit.
3. Which of the following is a property of definite integrals?
∫ (f(x) + g(x)) dx = ∫ f(x) dx - ∫ g(x) dx
∫ c * f(x) dx = c + ∫ f(x) dx
∫ f(x) dx = -∫ f(x) dx (from b to a)
∫ f(x) dx = f(b) - f(a)
4. Evaluate the definite integral: ∫ (from 1 to 3) 2x dx.
5. Consider the function f(x) = 4 shown in the graph below. Calculate the definite integral ∫ (from 0 to 5) 4 dx by finding the area of the shaded region.
6. The definite integral can be used to find the average value of a function over an interval.
True
False