Ap Calculus Jeopardy

Indefinite Integrals

100

∫2sec²(x)dx=?

2tan(x)+C

200

∫4sin(x)dx=?

−4cos(x)+C

300

∫(−3e^x+x⁴)dx=?

−3e^x+4ln∣x∣+C

400

∫(−3/x+3e^x)dx=?

−3ln∣x∣+3e^x+C

500

∫5csc²(x)dx=?

−5cot(x)+C

Definite Integrals

100

∫₁⁶2 dx=?

10

200

∫₀²(4x3−3x2+2x)dx=?

12

300

∫₋₁¹(12*3sqrt(x))dx=?

0

400

∫₀¹⁴ 10e^xdx=?

10e¹⁴−10

500

∫₂⁵(12−x^3/x⁴)dx=?

ln(5/2)−117/250

Integration using trigonometric identities

100

Evaluate ∫₀^π/2cos²x dx=?

π/4

200

∫tan³xdx=?

tan²x/2−ln∣secx∣+C

300

∫sin²xcos³xdx=?

(sin³x/3)−(sin⁵x/5)+C

400

∫sin⁴xdx=?

1/4(3/2x−sin²x+1/8sin⁴x)+C

500

∫₀^π/23cos³xdx=?

2

Integration with U-Substitution

100

∫4sin(x)/(3+cos(x)) dx=?

−4 ln(3+cos (x))+C

200

∫(x²)/(x³+4) dx=?

1/3ln∣x³+4∣+C

300

∫(2x+7)³ dx=?

(2x+7)⁴/8+C

400

∫(2x−5)¹⁰ dx=?

(2x−5)¹¹/22+C

500

∫(x)/sqrt(16-x²) dx=?

−sqrt(16−x²)+C

Motion Problems

100

As a particle moves along the number line, its position at time t is s(t), its velocity is v(t), and its acceleration is a(t)= 1.

If v(3) = -3 and s(2) = -10, what is s(4)?

-16

200

As a particle moves along the number line, its position at time t is s(t, its velocity is v(t) and its acceleration is a(t)=-cost. If v(π) = 2 and s(π/2)=-3π, what is s(0)?

1+2π

300

A particle with velocity v(t)=t²+3, where t is time in seconds, moves in a straight line.

How far does the particle move from t=2 to t=3 seconds?

28/3 units

400

The velocity of a particle moving along the x-axis is v(t)= 1/sqrt(t). At t=4, its position is 2.

What is the position of the particle, s(t), at any time t?

s(t)=2t^1/2−2

500

The velocity of a particle moving along the x-axis is v(t)=t²+t. At t=1 its position is 1.

What is the position of the particle, s(t), at any time t?

s(t)=1/3t³+1/2t²+1/6