AB Integral Flashcard

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).

Front

Define the term 'definite integral'.

Back

A definite integral is an integral that has specified upper and lower limits, representing the net area under the curve of a function between those limits.

Front

What does the symbol ∫ represent in calculus?

Back

The symbol ∫ represents the integral sign, indicating the operation of integration.

Front

Explain the concept of 'area under the curve' in relation to integrals.

Back

The area under the curve of a function f(x) from x=a to x=b is calculated using the definite integral ∫_a^b f(x) dx, representing the total accumulation of the function's values over that interval.

Front

What is an antiderivative?

Back

An antiderivative of a function f(x) is a function F(x) such that F'(x) = f(x). It represents the reverse process of differentiation.

Front

How do you calculate the integral of a constant?

Back

The integral of a constant c over the interval [a, b] is given by ∫_a^b c dx = c(b - a).

Front

What is the power rule for integration?

Back

The power rule for integration states that ∫ x^n dx = (x^(n+1))/(n+1) + C, where n ≠ -1 and C is the constant of integration.

Front

Define 'indefinite integral'.

Back

An indefinite integral is an integral without specified limits, representing a family of functions and includes a constant of integration, denoted as ∫ f(x) dx = F(x) + C.

Front

What is the relationship between integration and area?

Back

Integration is used to calculate the area under a curve, where the definite integral gives the exact area between the curve and the x-axis over a specified interval.

Front

Explain the concept of 'Riemann sum'.

Back

A Riemann sum is a method for approximating the total area under a curve by dividing it into rectangles, calculating the sum of their areas, and taking the limit as the number of rectangles approaches infinity.