integration review part i when you see the words this is what you think of doing a riemann sum...

Integration Review Part I

When you see the words… This is what you think of doing…

A Riemann Sum equivalent to the definite integral

is…

-

( )b

af x dx

10lim ( ) f or a x bx

f x x

1

Integration Review Part I

When you see the words… This is what you think of doing…

If f is continuous and bounded on an interval containing x = a and

F’(x) = f(x) for all x in the interval

( ) ( ) , then...x

aF x f t dt

2

Integration Review Part I

When you see the words… This is what you think of doing…

F (b) – F(a) where F’ = f

( )b

af x dx

3

Integration Review Part I

When you see the words… This is what you think of doing…

-( )a

bf x dx

4

( )b

af x dx

Integration Review Part I

When you see the words… This is what you think of doing…

-

5

( )c

af x dx

( ) ( )b c

a bf x dx f x dx

Integration Review Part I

When you see the words… This is what you think of doing…

f(x)

6

( )x

a

d f t dtdx

Integration Review Part I

When you see the words… This is what you think of doing…

f( g(x) ) * g’(x)

7

( ) ( )g x

a

d f t dtdx

Integration Review Part I

When you see the words… This is what you think of doing…

0

8

( )a

af x dx

Integration Review Part I

When you see the words… This is what you think of doing…

Trapezoid Rule -

9

( )b

af x dx

0 1 2 1( 2 2 ... 2 )2 n nh y y y y y

Integration Review Part I

When you see the words… This is what you think of doing…

If f is increasing on the interval [a,b], thena Left Riemann Sum (overestimates, underestimates) the true value of

Underestimates

10

( )b

af x dx

Integration Review Part I

When you see the words… This is what you think of doing…

If f is decreasing on the interval [a,b], thena Left Riemann Sum (overestimates, underestimates) the true value of

Overestimates

11

( )b

af x dx

Integration Review Part I

When you see the words… This is what you think of doing…

If f is increasing on the interval [a,b], thena Right Riemann Sum (overestimates, underestimates) the true value of

Overestimates

12

( )b

af x dx

Integration Review Part I

When you see the words… This is what you think of doing…

If f is decreasing on the interval [a,b], thena Right Riemann Sum (overestimates, underestimates) the true value of

Underestimates

13

( )b

af x dx

Integration Review Part I

When you see the words… This is what you think of doing…

If f is concave upward on the interval [a,b], then the Midpoint Riemann Sum (overestimates, underestimates) the true value of

Underestimates

14

( )b

af x dx

Integration Review Part I

When you see the words… This is what you think of doing…

If f is concave downward on the interval [a,b], then the Midpoint Riemann Sum (overestimates, underestimates) the true value of

Overestimates

15

( )b

af x dx

Integration Review Part I

When you see the words… This is what you think of doing…

If f is concave downward on the interval [a,b], then the Trapezoid Rule Sum (overestimates, underestimates) the true value of

Underestimates

16

( )b

af x dx

Integration Review Part I

When you see the words… This is what you think of doing…

If f is concave upward on the interval [a,b], then the Trapezoid Rule Sum (overestimates, underestimates) the true value of

Overestimates

17

( )b

af x dx

Integration Review Part I

When you see the words… This is what you think of doing…

Displacement (Integral)

.

18

( )b

av t dt

Integration Review Part I

When you see the words… This is what you think of doing…

.

19

nu du1

1nu C

n

Integration Review Part I

When you see the words… This is what you think of doing…

.

20

ue du ue C

Integration Review Part I

When you see the words… This is what you think of doing…

.

21

ue du ue C

Integration Review Part I

When you see the words… This is what you think of doing…

.

22

duu ln| |u C