
Definite Integrals
Flashcard
•
Mathematics
•
11th - 12th Grade
•
Practice Problem
•
Hard
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15 questions
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1.
FLASHCARD QUESTION
Front
What is a definite integral?
Back
A definite integral is a mathematical concept that represents the signed area under a curve defined by a function over a specific interval [a, b]. It is denoted as ∫_a^b f(x) dx.
2.
FLASHCARD QUESTION
Front
What is the Fundamental Theorem of Calculus?
Back
The Fundamental Theorem of Calculus links the concept of differentiation and integration, stating that if F is an antiderivative of f on an interval [a, b], then ∫_a^b f(x) dx = F(b) - F(a).
3.
FLASHCARD QUESTION
Front
Evaluate the definite integral: ∫_0^3 (2x + 1) dx
Back
The value of the definite integral is 12.
4.
FLASHCARD QUESTION
Front
What does the notation ∫_a^b f(x) dx represent?
Back
It represents the definite integral of the function f(x) from the lower limit a to the upper limit b.
5.
FLASHCARD QUESTION
Front
How do you find the area under a curve using definite integrals?
Back
To find the area under a curve, you calculate the definite integral of the function that describes the curve over the desired interval.
6.
FLASHCARD QUESTION
Front
Evaluate the definite integral: ∫_1^2 (x^2) dx
Back
The value of the definite integral is 5/3.
7.
FLASHCARD QUESTION
Front
What is the geometric interpretation of a definite integral?
Back
The geometric interpretation of a definite integral is the net area between the x-axis and the curve of the function f(x) over the interval [a, b].
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