This theorem allows calculations of area using
anti-derivatives.
What is The Fundamental Theorem
of Calculus?
“There is a c between a and b so that the tangent slope is the same as the secant slope” is
the conclusion of this theorem.
What is The Mean Value Theorem?
This theorem can be used to show that a continuous function must have a zero
on a specific interval.
What is the Intermediate Value Theorem?
What the theorem of integration of even and odd functions says that
. is equal to for an odd function.
What is Zero?
a
a
f (x)dx
This theorem says that
What is The Power Rule?
n 1n x
x dx Cn 1
e raised to this power is equal to 5.
What is ln 5?
What is ?x c
f (x) f (c)lim
x c
This is the formula to find the derivative of a function at c.
This is the sum of areas of rectangles whose heights are the outputs of a function.
What is a Riemann Sum?
The product of x and y even though y may vary.
What is a definite integral?
defines this value.
What is the average value of f(x) [on the interval from a to b] ?
b
a
1f (x)dx
b a
is the derivativeof this function.
What is 1/2 tan (2x)?
2sec (2x)
The integral which represents
What is ?
2ln | x | C
12 dx
x
is this.
What is ?
2x5 dx2x5
C2ln 5
The derivative of this type of function is always a constant.
What is a linear function?
This integral represents the area of a circle of radius 1.
What is ?1
2
1
2 1 x dx
This technique determines if a critical point is a relative extrema by checking the concavity at that point.
What is the Second Derivative Test?
This technique generates the formula for exponential
growth and is used to solve some differential equations.
What Separation of Variables?
In order to create a simpler integrand, one might use this
technique to rewrite the following:
What is u-substitution?
1
dxx 1 x
The act of making both sides of an equation into powers.
What is exponentiation?
A simple method used to approximate a definite integral.
Even an elementary school student could use this method.
What is counting squares?
This is added to all indefinite integrals.
What is a constant?
This is measured by the Second Derivative of a
function.
What is concavity?
A function being differentiable implies
that it is this also.
What is continuous?
This allows f(g(x)) to be differentiated.
What is the Chain Rule?
A conditional statement whose “if” and “then” parts
have been switched.
What is the converse of the statement?
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