Integration

Common Integrals

100

ƒ sinx dx

What is -cosx + c

200

ƒ e^x dx

What is e^x + c

300

ƒ 1/x dx

What is lnx + c

400

ƒ csc²x dx

What is -cotx + c

500

ƒ a^x dx

What is (a^x)/(ln(a))

Antiderivatives

100

f(x) = -3

F(x) = -3x + c

200

f(x) = -6x

F(x) = -3x² + c

300

f(x) = -24x⁵ - 10x

F(x) = -4x⁶ - 5x² + c

400

f(x) = 4x^-5

F(x) = -1/x⁴ + c

500

f(x) = -2x^-3 +20x^-5

F(x) = 1/x² - 5/x⁴ + c

Indefinite Integrals

100

ƒ 3 dx 

What is 3x + c

200

ƒ x² dx 

What is x³/3 + c

300

ƒ 5x⁴ + 2 dx 

What is x⁵ +2x + c

400

ƒ -9x² + 10x dx

What is -3x³ + 5x² + c

500

ƒ(-2x^-3)dx

What is 1/x² + c

Vocab

100

ƒ What is this symbol called?

What is the integral symbol

200

Definite Integrals find the area/value between the curve and the ......

What is the x-axis

300

What is an antiderivative also called?

What is an indefinite integral

400

What do you find when you solve an indefinite integral?

What is an antiderivative

500

In the following equation what is f(x) called? ƒ f(x) dx

What is the integrand

Differential Equations

100

f'(x) = 3x - 1 , f(2) = 5 

F(x)= (3x²)/2 - x + 1

200

f'(x) = 2sinx, f(pi/2)= -3

F(x) = -2cosx - 3

300

f'(x) = 3x² - 4x + 2 , f(-1) = -4

F(x) = x³ - 2x² + 2x +1

400

g'(x) = sqrt(x) , g(9) = 6

G(x) = 2t^2/3/3 - 12

500

f'(x) = sinx, f(0) = 2

F(x) = -cosx + 3