ws: riemann sums. test topics: area and definite integration find area under a curve by the limit...

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WS: Riemann Sums 100 0 202.8 4.0 4. 1) a 7 5.1 52 ) 36 . 4 f t dt 100 0 20 1.2 2. b) 35 8 4.0 4 5.1 6 .7 f t dt 60 0 10 400 15 350 12 280 9 200 14 1 2) 16,930 gal 80 f t dt 50 0 10 12 30 70 8 3) 2530 60 ft 1 vt dt 24 0 6 10.4 11.2 11.3 10 4) .2 258.6 gal Rt dt 90 0 30 20 10 30 10 40 20 55 5) 3700 g l 65 a 20 Rt dt

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Use the First and Second Fundamental Theorems of Calculus. –Integrals involving trig –Integration by substitution –Etc. Find the average value of a function. TEST TOPICS: Area and Definite Integration

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Page 1: WS: Riemann Sums. TEST TOPICS: Area and Definite Integration Find area under a curve by the limit definition. Given a picture, set up an integral to calculate

WS: Riemann Sums 100

0 20 2.8 4.0 4.1) a 7 5.1 5 2)36

.4

f t dt

1000 20 1.2 2.b)

358 4.0 4 5.1

6.7f t dt

600 10 400 15 350 12 280 9 200 14 12)

16,930 gal80f t dt

500 10 12 30 70 83)

2530 60

f t1v t dt

240 6 10.4 11.2 11.3 104) .2

258.6 galR t dt

900 30 20 10 30 10 40 20 555)

3700 g l65

a20R t dt

Page 2: WS: Riemann Sums. TEST TOPICS: Area and Definite Integration Find area under a curve by the limit definition. Given a picture, set up an integral to calculate

TEST TOPICS:Area and Definite Integration• Find area under a curve by the

limit definition.• Given a picture, set up an

integral to calculate area.• Calculate right-handed, left-

handed, and midpoint Riemann sums from a table.

Page 3: WS: Riemann Sums. TEST TOPICS: Area and Definite Integration Find area under a curve by the limit definition. Given a picture, set up an integral to calculate

• Use the First and Second Fundamental Theorems of Calculus.

– Integrals involving trig– Integration by substitution– Etc.

• Find the average value of a function.

TEST TOPICS:Area and Definite Integration

Page 4: WS: Riemann Sums. TEST TOPICS: Area and Definite Integration Find area under a curve by the limit definition. Given a picture, set up an integral to calculate

• Use the Trapezoidal Rule to approximate an integral.

• Part w/ calculator, part without.• Wear FALCON CALCULUS shirt.

TEST TOPICS:Area and Definite Integration

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