Integrals

Function for f

100

f'(x)=(1/5)x-2 f(10)=-10

f(x)=[(X^2)/10]-2x

200

f'(x)=(2x-3)(2x+3) f(3)=0

f(x)=[(4x^3)/3]-9x-9

300

* f'(x)=3(x^1/2)+3 f(1)=4

f(x)=2(x^3/2)+3x-1

400

f(x)=6x(x-1) f(1)=-1

f(x)=2(x^3)-3(x^2)

500

f(x)=(2-x)/(x^3) x>0 f(2)=3/4

f(x)=[-1/(x^2)]+(1/x)+(1/2)

Trig

100

∫xcos[2(x^2)]dx

1/4sin[2(x^2)]+C

200

∫(e^x)sin(e^x)dx

-cos(e^x)+c

300

∫sec(2x)tan(2x)dx

1/2sec(2x)+C

400

∫[(csc^2)x]/[(cot^3)x]dx

1/2(cot^2)x+C

500

∫tan2xdx

-1/2ln│cos(2x)│+C

Indefinite

100

∫4/xdx

4ln│x│+C

200

∫1/(2x-1)dx

1/2ln│2x-1│+C

300

∫[(x^2)+(2x)+3]/[(x^3)+(3x^2)+(9x)+1)]dx

1/3ln│(x^3)+(3x^2)+(9x)+1│+C

400

∫(x^3)/[(1+(x^4))^(1/3)]

3[(1+(x^4))^(2/3)]/8+C

500

∫[(x^2)+x+1]/(x-1)dx

[(x^2)/2]+2x+3ln│x-1│+C

Definite

100

∫1/xdx [1,2]

0

200

∫[(x^2)+1]dx [-1,3]

40/3

300

∫e^(2x)dx [0,3]

201.214

400

∫(2x+3)^3 dx [0,1]

68

500

∫√(2/x)dx [1,4]

2√8 5.657

Word Problems

100

A ball is dropped from near the top of the Empire State Building, at a height 960ft above 34th street, How long does it take for the ball to reach the street and with what elocity does it strike the street?

t=√60 v(60)=-247ft/s

200

The marginal cost for producing x-units of a product is modeled by dC/dx=32-0.04x. It cost $50 to produce one unit. Find the total cost of producing 200 units.

$5,618.02

300

A ball is thrown upwards with an initial velocity of 64 feet per second from an initial height of 80 feet. Derive the position function giving the height s (in feet) as a function of time t (in seconds). When does the ball hit the ground? Use a(t)=-32 feet per second squared.

t=5s

400

The Grand Canyon is 6000 feet deep at the deepest part. A rock is dropped from this height. Express the height of the rock as a function of time t (in seconds). How long will it take the rock to hit the canyon floor?

t=√375

500

A balloon, rising vertically with a velocity of 16 feet per second, releasing a sandbag at the instant when the balloon is 64 feet above the ground. a. How many seconds after its release will the bag strike the groung? b. With what velocity will the bag strike the ground?

a. t=2.56s b. v(t)=-65.92 ft/s