Review First Partial

A

100

int(6x−4)(3x^2-4x)^5dx

1/6 (3x^2-4x)^6 + C

200

int (6x^2 - 5x^5 + 8x^3 + 4sqrtx) / (2x^3) dx

3ln |x| - 5/6x^3+4x-2/sqrtx+C

300

∫18e^(3x)sqrt(e^(3x) −5) dx

4(e^(3x)-5)^(3/2) + C

400

∫ [ 4 /t^2 tan ⁡ ( 3/t ) sec ⁡ ( 3/ t ) + 10^(2t) ] d t

-2/3 sec (3/t) + 10^(2t) / 2ln10 + C

500

∫12e^3x[sec²(e^3x)−2]dx

4tan(e^3x) - 8e^3x+ C

Teacher info

100

What is the phrase the teacher says to get attention?

Raise your hand if you can hear me

200

How old is the teacher?

26

300

What musical did the teacher saw last year?

Hamilton

400

When is the teacher birthday?

May 13th 

500

What are the teacher's favorite flowers?

Sunflower, tulips, Hydrangeas

B

100

int 12x^2-6x dx

4x^3-3x^2+C

200

int sin(1/x)/x^2 dx

cos(1/x) + C

300

The rate of change of the volume of a balloon is

(dV)/dt = 3t^2 + 2t

 If initially the volume is 5 cm³, find the volume at time t.

V(t)=t^3+t^2+5

400

Evaluate 

int x/(1+x^4) dx

1/2 arctan (x^2)+C

500

The growth rate of a bacteria population is

(dP)/dt=15/(sqrt(2t+4)

 bacteria/day. The initial population is 500. Find the population equation.

P(t)=15sqrt(2t+4) + 470

Random facts

100

What is the capital of Australia?

Canberra

200

Which planet is known as the "Red Planet"?

Mars

300

The chemical symbol for gold on the periodic table is:

Au

400

The Great Wall of China was primarily built to protect against invasions from which historical group?

The Mongols

500

At the 2022 Grammy Awards, which album won "Album of the Year," making the artist the second ever to win this category three times?

*30* – Adele

C

100

f'(x)=sec^2 x+1

f(x)= tan x + x +C

200

Evaluate

int 3^(2x)/5dx

 

(3^(2x))/(10ln3)+C

300

Evaluate 

int cosx/(1+sin^2x) dx

arctan(sinx) +C

400

The marginal cost to produce x items is

C'(x)=0.3x^2-2x+50

. If the fixed cost is $1000, find the cost function.

C(x)=0.1x^3 - x^2+50x +1000

500

Find f(x) if 

f''(x)=2+12x^2, f'(0)= -1, and f(0)=5

f(x)=x^2+x^4 -x +5