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AP Calculus-Integrals and Antiderivatives

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Section 1

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integral of sinx

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Calculus Math

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Mar 1, 2020

Cards (20)

Section 1

(20 cards)

integral of sinx

Front

-cosx + c

Back

Integral from a to a is ___________________.

Front

0

Back

integral of cosx

Front

sinx + c

Back

definite integral

Front

Back

2nd Fundamental Theorem of Calculus

Front

If f is continuous on an open interval I containing a, then for every x in the interval (d/dx) integral from a to x of f(t) dt = f(x).

Back

integrand

Front

a function that is to be integrated.

Back

When integrating right to left the integral will be _________________.

Front

Negative

Back

Indefinite integral

Front

Back

1st fundamental theorem of calculus

Front

If f is continuous on [a,b] and F is an antiderivative of f on [a,b], then integral from a to b of f(x) dx = F(b) - F(a).

Back

integral of secxtanx

Front

secx + c

Back

integral of sec^2(x)

Front

tanx + C

Back

right-hand sum

Front

a rectangular sum of the area under a curve where the domain is divided into sub-intervals and the height of each rectangle is the function value at the right-most point of the sub-interval

Back

Midpoint Sum

Front

a rectangular sum of the area under a curve where the domain is divided into sub-intervals and the height of each rectangle is the function value at the midpoint of the sub-interval

Back

When integrating left to right the integral will be _________________.

Front

Positive

Back

Trapezoidal Rule

Front

Integral (a to b) = ((b-a)/2n)(f(x)+2f(x)+2f(x)+f(x))

Back

Antiderivative

Front

a function F(x) is an ________________________ of a function ƒ(x) if F'(x)=ƒ(x) for all x in the domain of ƒ

Back

Mean Value Theorem for Integrals

Front

Back

integral of csc^2(x)

Front

-cotx + c

Back

left-hand sum

Front

a rectangular sum of the area under a curve where the domain is divided into sub-intervals and the height of each rectangle is the function value at the left most point of the sub-interval

Back

Integral of cscxcotx

Front

-cscx + C

Back