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Basic Integration Formulas
Differentiation
Rules
Trigonometry Identities
Areas Under a Curve
Polar Coordinates
100
The equivalent of u+c.
What is ∫du?
100
The equivalent of d/dx[cu].
What is cu'?
100
The family of identities that sin(x)=1/(csc(x)) belongs to.
What are reciprocal identities?
100
The crudest and least accurate method used to find areas under a curve.
What are Riemann Sums?
100
The variable used in place of y for polar coordinates as apposed to x,y-coordinates.
What is r?
200
The same as -cos(u) + c.
What is ∫sin(u) du?
200
The derivative of e^u.
What is e^u?
200
The mathematical equivalent of tan(2u).
What is (2tan(u))/(1-tan^2(u))?
200
The usual method used to find the two dimensional area under a curve.
What is integration?
200
The polar curve that is identified by the inner loop within the greater shape.
What is a limacon?
300
The integration of ∫csc(u) cot(u) du.
What is -csc(u) + c?
300
The same as u'/(1+u^2).
What is d/dx[arctan(u)]?
300
The identities that state that sin^2(x) + cos^2(x) = 1.
What are Pythagorean identities?
300
The method used to find the three dimensional area between two curves.
What is the shell method.
300
The equation for area in polar coordinates.
What is 1/2∫r^2dθ?
400
The reduction of ∫a^u du.
What is (1/ln(a))a^u + c?
400
The equivalent of d/dx[sec(u)]
What is -(sec(u)tan(u))u'?
400
The reduction of sin(-x).
What is -sin(x)?
400
The formula for the area of a surface of revolution.
What is 2π∫f(θ)sin(θ)√(f(θ)^2 + f’(θ)^2)dθ?
400
The five main polar shapes.
What are circles, cardiods, limacons, dimpled limacons, and roses?
500
The anti-derivative of (1/a)arctan(u/a) + c.
What is ∫du/(a^2 + u^2)?
500
The rule that means you find the derivative of the inside and outside equations, then multiply them.
What is the chain rule?
500
The product-to-sum of sin(u)cos(v).
What is 1/2[sin(u+v) + sin(u-v)]?
500
What term is indicative of a problem concerning the area of geometric shapes rotated around a curve?
What are perpendicular cross-sections?
500
The shape drawn by r = 3cos(3θ).
What is a three petaled rose?