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Trapezoid and Riemann sums and definite integrals Cheat Sheet (DRAFT) by

Calculus semester 2 quiz 1

This is a draft cheat sheet. It is a work in progress and is not finished yet.

Review of integrals

U substi­tution
1. define u 2.write derivative of u 3. simplify to cancle 4. sub in 5. integrate
Integr­ation
1. add 1 to exponent of x and multiple by reciprocal of exponent
cos
sin
sin
-cos
sec^2
tan
sectan
sec
csc^2
-cot
csccot
-csc
e^x
e^x
b^x
b^x/lnb
1/x
lnIxI

Trapezoid sums

Area of a trapezoid
A=1/2 (b1+b2)h
1.
divide top #- bottom # by number of subint­ervals
2.
Create number­line, plug in numbers
3.
Plug into area equation, bases are numbers on numberline and height is the distance between them
4.
Add all subint­ervals together
Undere­stimate
some left out, double derivative is negative, so concave down
Overes­timate
Concave up

Definite Integrals

1.
find antide­riv­ative (integrate function and dake away dx, line with top and bottom values
2.
Plug in upper value to integrated expression
3.
Plug in lower value to integrated expression
4.
Subtract lower value from upper value
 

Midpoint Riemann Sums

1.
divide top #- bottom # by number of subint­ervals
2.
numberline
3.
find middle of each of the points
4.
Plug in each midpoint to given equation
5.
add midpoints together

DrawRect calculator program

1.
enter equation into y= section
2.
set approp­riate window, program button, enter
3.
partion= number of subint­ervals
4.
select method

Left and Right Riemann sums

Left
left value is plugged into equation
Right
right value is plugged into equation

Definite Integrals with U-subs­tit­ution

1.
Identify u and solve for derivative
2.
Plug in top and bottom number to original u equation and replace in integral
3.
Rewrite integral
4.
Integrate
5.
Plug in new top value to integrated expression
6.
Plug in new bottom value to integrated expression
7.
Subtract top expression from bottom expression

Sigma Notation

1.
Pick a number to be your n (ex.4)
2.
Divide top #- bottom # by n
3.
number line from bottom number to top with divided distance
4.
plug in intervals to equation (right left or mid) and multiply by distance
5.
Add interval equation values together
6.
Equation answer is sigma n on top k=1 on bottom, given equation with first interval +distance times k inside