Payt ( more ) calc I Some review about talks Calculus I of The - - PowerPoint PPT Presentation

Payt

Some

(more )

calc I

review

The

end

• f

Calculus I

talks

about

the

area

problem(

area

• afbflxldx

#

y=fCx)

¥¥¥÷÷÷÷÷÷÷÷÷÷

. Goal

:

area

• f

yellow

figure

Good

news :

we

know

how to

compute

areas of

reduyles

Bad

news

:

almost

all

• ther

areas are

hard, and

most

graphs of

function

,

an

"

rectangular

"

• r

" circular "

⇐ ' " ¥±¥"÷÷: :÷÷÷÷

:

" basic "

geometry

Resolution

:

we

can

approximate

areas

pretty easily

a-

Substitute

the

actual

Indian

with

"

step Anakin

"

① divide enteral lab]

into

n

sub intervals

• f width

DX

• b
• ffxj)

it

• n

::x÷

:.in#i:* X

i

:÷÷÷÷÷:÷÷÷÷link

.

a

height

width

n

• m

Idea :

fab Hxldx

I ?

flxit)

DX

• ✓

area of rectangle

actual

area

• ver

ith sobmtonal

a

new add

them

up

Good

news : has good

geometric

intuition & very computable

Belter

news

:

labflxldx

=

'

n'I. Ee

flxi) DX

Bad

news

'

n'Ia 7 flxi) Dx

is

really

really

really

really really really really really really really

hard

( generally

speaking ) to

compute (In but

, often

impossible )

Salvati

there's

another

way to

compute

area

without

limits

• f

Riemann

sums

them

(Fundamental

Theorem of Calculus

, part II)

Suppose

flx)

is

continuous

an

[ a , b)

and

f- (x)

is

an

ant durative

for

Hx)

• n la , b)

( ie ,

HIFK))

• Hx) for

all

x

in

land)

{ flxldx

= f- ( b)

• Fla)

Good

news : if

you

can find

antidunlins

can

compile

areas .