Indefinite Integrals
xn dx
xn+1 / n+1 +C
how do we find indefinite integrals
find ALL antiderivatives
difference between Rn and Ln
determines which top corner is touching the curve
integration and [blank] are inversely related
differentiation
sin(x) dx
-cos(x) + C
which indef. integrals are negative
sin(x) dx; csc2(x) dx; csc(x) cot(x) dx
looking on a graph, which value of x do we use first
if finding Right sums, use the second x
if using left sums, use the first x
what happens when you take the derivative of a definite integral
you take the inner function and find antiderivative
cos(x) dx
sin(x) + C
csc2(x) dx
-cot(x) + C
how do we find reemann sums
take diff. of x's multiplied by x ran through the function
is chain rule allowed
YES
sec(x) tan(x) dx
sec(x) + C
is chain rule allowed
no, we FOIL
Rn =
sum (from k=1 to n) of delta x times f(xk)
for definite integrals, what dose plug into the variable
the number on top of the fancy S
csc(x) cot(x) dx
-csc(x) + C
what is Maddie's favorite candy
sweet tart ropes
definite integrals (S f(x) dx) equal
Rn as n approaches infinite
how do we annotate after taking derivative of definite integral
first by replacing big fancy S with a bar on the right,
then once we've found the antiderivative,
we find the difference of f(a) and f(b)