Calculus 1 Vocab - Chapter 4

Antiderivative

The process of finding the original function when given the derivative

Differential equation

An equation that contains the derivative of a function in it

Indefinite Integration

Same as the antiderivative

Relationship of distance to velocity and acceleration

 v(t)dt = d(t), a(t)dt = v(t), a(t) = v’(t), v(t) = d’(t), a(t) = d”(t)

Riemann Sum

The process of approximating the area under the curve by using small rectangles

Average Value of a Function

Fundamental Theorem of Calculus

Suppose that f is continuous on [a, b], Part I: If F is defined on [a, b] by (average value of a function) then F is an antiderivative of f. That is, F’(x) = f(x) for x in [a, b]. Part II: If G is any antiderivative of f on [a, b], then…

Simpson’c Rule

1/3 (∆x) (Y0 + 4Y1 + 2Y2 + 4Y3 + 2Y4 +...+ 2Yn-2 + 4Yn-1 + Yn) and n is even; or 1/3(2M + T)

Trapezoid Rule

Half the first height, plus all the other heights, plus half the last height, all multiplied by the width