Integration and Definite Integrals (5.1-5.2) Flashcards
The antiderivative of a function blank is a function blank
f(x) and F(x)
F prime = f(x)
Integration Theorem
if f(x) and g(x) are antiderivatives of the same function then f(x) and g(x) differ by constant c
Indefinite integrals always need
+c
Integral of c f dx
c integral f dx
Integral of f + g dx
Integral f dx + Integral g dx
Integral of 0
c
Integral 1 dx
x + c
Integral x^n dx
(1/n+1) x^n+1 +c
Integral cosx
sinx +c
Integral sinx
-cosx +c
Integral secx squared
tanx +c
Integral cscx cotx
-cscx +c
Integral secx tanx
secx +c
Integral cscx squared
-cotx + c
Integral of e^x
e^x +c
Integral a^x
a^x / lna +c
Integral 1/x
ln x +c
How do you solve an initial value problem (given two different initial values and only given one)
- take integral of rate/derivative given
- plug in initial value
- solve for c
- plug in c
- do as many times as given a rate of
definite integral vs indefinite integral
definite has bounds while indefinite has plus c
a definite integral is defined on
closed interval a to b
Area above x-axis is blank and area below x-axis is blank
positive, negative
Integral from a to a of f
0
integral from a to c of f
Integral from a to b of f + Integral from b to c of f
Integral from b to a of f
- Integral from a to b of f
Integral from a to b of f+g
Integral from a to b of f + Integral from a to b of g
Integral from a to b of xf
x Integral from a to b of f
how to find missing integral value
watch out for bounds
1. how much they = to
2. which way bounds are going
For problems where you need to find a missing integral…
use a number line to visualize it
Equation for top/bottom half of circle
a or integral from x to x = square root of r squared minus x squared
