AP Calculus: Semester 2

Evaluating Integrals

100

∫ cosΘ dΘ

sinΘ + C

200

∫ sinΘ dΘ

-cosΘ + C

300

∫ (-4t + 7) dt

-2t² + 7t + C

400

∫⁷₃ (4 - 2x) dx

-24

500

∫ 1 / (36 + (x+4)² dx

⅙ arctan (x-4)/6 +C

Slope Fields

100

What shape does dy/dx = x create?

Parabola

200

What shape does dy/dx = y create?

logarithmic shape

300

What shape does dy/dx = x² create?

Cubic Function

400

What shape does dy/dx = -x/y create?

Circle

500

What shape does dy/dx = sin(x) create?

Cosine Graph

Disk & Washer

100

Is V = π∫_a ^b ([R(x)]² - [r(x)]²) dx disk or washer?

Washer

200

Is V = π∫_a ^b ([R(x)]² dx disk or washer?

Disk

300

Find the volume of the solid by rotating the region bounded by f(x) = 4√x , the x-axis, and the line x= 4

16π / 3

400

Find the volume of the solid obtained by rotating the region bounded by f(x) = √x, the x-axis, and x=1

π/2

500

Find the volume of the solid obtained by rotating the region bounded by g(x)=x³ and h(x)= √x around the horizontal line y=-2

π ∫¹₀ (√x+2)² - (x³ + 2)²) dx

L' Hospital's

100

lim √(1 + x) -1 - (x/2)

^{x -> 0}

0

200

lim (2 sin(3x) + sin(5x)) / 2x

^{x -> 0}

11/2

300

lim (1-x²) / ln(x)

^{x -> 1}

-2

400

lim (sinx) / (5x + 3 sinx)

^{x -> 0}

1/8

500

lim (1 - e^x) / (ln (2 - e^x))

^{x -> 0}

1

Random

100

cos(3π/2)

0

200

What is the formula used to find the area of a circle?

A = πr²

300

sin(60°)

√3/2

400

What is the equation of a circle?

(x - h)² + (y - k)² = r²

500

What is the Fundamental theorem of calculus?

∫ ^b_a f(x) dx = F(x) |^b_a = F(b) -F(a)