Calculus 2 FInal Exam FOrmulas

Integration by Parts Equation

What acronym use to categorize the parts of Integration by Parts

LIATE - Log, Inverse, Algebraic, Trig, Exponential

What is the trigonometric Identity of sin²x + cos²x?

sin²x+cos²x = 1

What is the trigonometric identity of Sin(2x)?

Sin(2x) = 2sin(x)cos(x)

What is the trigonometric identity of tan²x + 1?

tan²x + 1 = sec²x

What is the trigonometric identity of cot²x + 1?

cot²x + 1 = csc²x

What is the trigonometric substitution for √a²-x²

x = a sin(θ)

What is the trigonometric substitution for √a²+x²

x = a tan(θ)

What is the trigonometric substitution for √x²-a²

x = a sec(θ)

What are the rules for Trigonometric Substitutions?

1. Find what x is by looking for the correct trig-sub formula. Then, put whatever a is under the x, and create a triangle based off of the θ that the trig.sub is.

2. Plug in the x’s into the original equation

3. Simplify by using trigonometric integral identities as much as you can.

4. Take the integral with the theta identities

5. Plug back in x for theta by following the triangle you have made.

What is the formula for finding area between curves when it asks you a y = x² equation and a y = x equation?

∫ f(upper) - f(lower) dx

What is the formula for finding area between curves when it asks, for example, a x = y² equation and a x = y equation?

∫ f(right) - f(left) dy

What is the formula for volume equations?

What is the formula for volume equations for when there is an inner/outer radius? i.e, y = 3e^−x, y = 3, x = 2

(If the x is above/right of the function, it goes in front. If the x is below/left of the function, it goes to the back)

π∫ (2 - 3e^-x)

What is the equation to find volumes by “using the method of cylindrical shells”?

2π∫ x(f(x)) dx

What is the formula for arc-length?

What is the formula for the surface area of revolution?

(Where r is 1)

What is the equation for finding the area using polar coordinate values?

A = ∫1/2 * r² d(Θ)