HS Calculus S2 Jeopardy

Definite Integrals

100

find -2∫4 |x| dx

10

200

 0∫pi (sin x+2) dx

2pi + 2

300

Approximation of the definite integral -2∫1 (x^2+2) dx with a Riemann sum using three equal subintervals and the right endpoints

8

400

 -1∫3 (2x+1)² dx

57 1/3

500

0∫3 f(x) dx = 1, 3∫7 f(x) dx = -4, 

0∫1 f(x) dx = 2

7∫1 f(x) dx

5

Techniques of Integration

100

u and dv for ∫x ln x dx

u=ln x and dv=x

200

Trig substitution used for ∫1/√ (9-x²) dx

x=3sinθ 

300

∫(x-9)/(x²+3x-10) dx

2 ln|x+5| - ln|x-2| + C

400

∫x/(x² - 1) dx

1/2 ln|x² - 1| + C

500

∫ cos³x dx

sinx - (1/3) sin³x + C

Geometric Applications

100

Method that uses circles to calculate volume if there is a hole in the figure

washer method

200

This integral is used to find areas between two curves with respect to y

What is a∫b  (right - left) dy

300

Length of an arc of the parabola x=y² from (0,0) to (1,1)

approximately 1.479

400

Volume of the solid for the region bounded by y=√x and y=x rotated about the line y=1

pi/6

500

Area bounded by y=x² and y=2/(x²+1)

pi - 2/3

Differential Equations

100

The graphical depiction of a differential equation

Slope Field

200

s(t) if v(t) = 24t^3 - 12t^2 + 2t and s(1)=0

s(t) = 6t^4 - 4t^3 + t^2 - 3

300

dx if you use Euler's Method to approximate y(2) using 4 steps given y(0)=1

dxd=0.5

400

y if dy/dx = e^xy²

y= 1/(-e^x + C)

500

The difference when $3000 is invested at 5% interest for 2 years compounded weekly compared to compounded continuously

16 cents

Misc

100

4∫x² (tan t) dt

2x tan(x²)

200

the average value of a function

1/(b-a) a∫b f(x) dx

300

1∫∞  1/x² dx

1

400

d/dx [tan^-1 (e^x)]

e^x/(1+e^2x)

500

1∫2 x√(x-1) dx

16/15