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 'antiderivative'.

Back

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

Front

What is the area under a curve?

Back

The area under a curve f(x) from x = a to x = b is given by the definite integral ∫_a^b f(x) dx.

Front

Explain the concept of definite integral.

Back

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

Front

What does the symbol ∫ represent?

Back

The symbol ∫ represents the integral sign, used to denote the process of integration.

Front

What is the difference between definite and indefinite integrals?

Back

A definite integral has specific limits and results in a number, while an indefinite integral has no limits and results in a function plus a constant of integration.

Front

How do you find the integral of a constant?

Back

The integral of a constant c with respect to x is cx + C, where C is the constant of integration.

Front

What is the power rule for integration?

Back

The power rule states that ∫x^n dx = (x^(n+1))/(n+1) + C, for n ≠ -1.

Front

What is the integration of sin(x)?

Back

The integral of sin(x) is -cos(x) + C.

Front

What is the integration of e^x?

Back

The integral of e^x is e^x + C.