Integral Calculus

1 + tan² x=?

sec²(x) Which Pythagorean formula = sec²(x)?

∫ cos x dx?

sin x + c is the integral of what?

∫ cosh(x) dx

sinh(x) + C Is the integral for what?

∫ sech(x) dx

sin⁻¹ (tanh(x)) + C Is the integral for what?

sin(pi/4)=?

sqrt of 2 divided by 2 is the arcsin of what?

sin(pi/3)=?

sqrt of 3 divided by 2 is the arcsin of what?

tan(pi/3)=?

sqrt(3) What is the arctan of the sqrt of (3)?

∫ sec² x dx?

tan x + c is the integral of what?

∫ tan² x dx?

tan x - x + c is the integral of what?

cos(pi/4)=?

the sqrt of 2 divided by 2 is the arccos of what?

cos(pi/6)=?

the sqrt of 3 divided by 1/2 is the arccos of what?

tan(pi/6)=?

the sqrt of 3 divided by 3 what is the arctan of sqrt(3)/3?

tan(pi/2)=?

undefined in the first quadrant where is the arctan undefined?

sin(0)=?

0 is the arcsin of what?

tan(0)=?

0 what is the arctan of 0?

tan(pi/4)=?

1 What is the arctan of 1?

sin²x + cos² x=?

1 Which Pythagorean formula = 1?

cos(0)=?

1 is the arccos of what?

sin(pi/2)=?

1 is the arcsin of what?

d/dx (sec x)?

sec x tan x is the derivative of what?

d/dx (tan x)?

sec² x is the derivative of what?

∫ csc² x dx?

- cot x + c is the integral of what?

∫ csc x cot x dx?

- csc x + c is the integral of what?

d/dx (cot x)?

- csc² x is the derivative of what?

d/dx (cos x)?

- sin x is the derivative of what?

∫ sin x dx?

-cos x + c is the integral of what?

d/dx (csc x)?

-csc x cot x is the derivative of what?

∫ tan x dx?

-ln |cos x| + c is the integral of what?

∫ csc x dx?

-ln |csc x + cot x| + c is the integral of what?

sin(-x)=?

-sin x -sin(x) = sin(-x) or only -sin(x)?

cos(pi/2)=?

0 is the arccos of what?

cos(pi/3)=?

1/2 is the arccos of what?

sin(pi/6)=?

1/2 is the arcsin of what?

Integral of 1/a^2+x^2 dx

1/a arctan (x/a) + C Is the integral for what?

∫ dx/(a² + x²)?

1/a arctan (x/a) + c is the integral of what?

Integral of 1/(a^2-x^2) dx

1/a arctanh (x/a) + C Is the integral for what?

d/dx (ln x)?

1/x is the derivative of what?

d/dx f(g(x)) Rule?

Chain Rule When do you use the chain rule?

What is the formula for Hooke's Law?

Hooke's Law: F=kd is force (f) equals the spring constant (k) times the distance (d).

d/dx arccos(x)?

Is the derivative for what?

d/dx arccot(x)?

Is the derivative for what?

d/dx arccsc(x)?

Is the derivative for what?

d/dx arcsec(x)?

Is the derivative for what?

Formula for sinh(x)?

Is the formula for what function?

What is the formula for cosh(x)?

Is the formula for what function?

What is the formula for coth(x)?

Is the formula for what function?

What is the formula for csch(x)?

Is the formula for what function?

What is the formula for sech(x)?

Is the formula for what function?

What is the formula for tanh(x)?

Is the formula for what function?

Formula for integrating about the line x=0 using the shells method?

Is the formula for what?

The formula for arccosh(x)?

Is the formula for what?

What is the formula for a collection of masses along a straight line?

Is the formula for what?

What is the formula for integrating about the line y=0 using the shell method?

Is the formula for what?

Arc Length Formula?

Is the integral for what?

Surface Area Formula?

Is the integral for what?

d/dx (x^n) Rule?

Power Rule Reverse the power rule for derivatives.

d/dx (f/g) Rule?

Quotient Rule When do you use the quotient rule?

∫ sec x tan x dx?

sec x + c is the integral of what?

∫ a^x dx?

a^x/ ln a + c is the integral of what?

Integral of 1/sqrt(x^2-a^2) dx

arccosh (x/a) + C Is the integral for what?

∫ dx/(sqrt(a² - x²))?

arcsin (x/a) + c is the integral of what?

integral of 1/sqrt(a^2-x^2) dx

arcsin of (x/a) + C Is the integral for what?

Integral of 1/sqrt(a^2+x^2) dx

arcsinh of (x/a) + C Is the integral for what?

∫ a dx?

ax + c is the integral of what?

d/dx (sin x)?

cos x is the derivative of what?

∫ sinh(x) dx

cosh(x) + C Is the integral for what?

1 + cot² x=?

csc² x Which Pythagorean formula = csc² x

∫ e^x dx?

e^x + c is the integral of what?

d/dx (f*g)

fg' + gf' Product Rule What is the product rule in reverse?

d/dx (a^x)?

is the derivative of what?

d/dx (arcsec x)?

is the derivative of what?

d/dx (e^x)?

is the derivative of what?

d/dx arcsin (x) ?

is the derivative of what?

d/dx arctan (x) ?

is the derivative of what?

Formula for integrating using the disk method?

is the formula for what?

Formula for integrating using the washer method?

is the formula for what?

The formula for arcsinh? (x)?

is the formula for what?

The formula for arctanh?

is the formula for what?

The formula for the arccoth?

is the formula for what?

The formula for the arccsch?

is the formula for what?

The formula for the arcsech?

is the formula for what?

∫ 1/x dx?

ln | x | + c is the integral of what?

∫ sec x dx?

ln |sec x + tan x| + c is the integral of what?

∫ cot x dx?

ln |sin x| + c is the integral of what?

∫ coth(x) dx

ln |sinh(x)| + C Is the integral for what?

∫ csch(x) dx

ln |tanh(x/2)| + C Is the integral for what?

∫ tanh(x) dx

ln(cosh(x)) + C Is the integral for what?

Surface Area of a Sphere?

where a is a constant Is the formula for what?

∫ ln x dx?

x ln x - x + c is the integral of what?

What is the area of a circle geometrically?

π(a²) a=radius is the area of what?