Derivative
f(x)=6x3-9x+4x1/2
f'(x)=18x2-9+2x-1/2
INT[sin(x)]
-cos(x)+C
What formula is this?
f'(x)=n(x)n-1
Derivative
x 1 2 3 4 5 6
y 5 7 9 11 13 15
Calculate the Left Riemann Sum
45
Vertical Washer Formula
pi[INT(a,b)]R2-r2
f(x)=2x5−10x4+13x3−10x2+13x
f'(x)=10x4-40x3+39x2-20x+13
INT[f(x)dx]= 10 INT[f(x)dx]= 20
[5,10] [0,15]
INT[f(x)dx]= -5
[10,15] What is [0,5]?
INT[f(x)dx]= 15
What formula is this?
f(x)=(xn+1)/n+1
Integral Formula
x 1 2 3 4 5 6
y 5 7 9 11 13 15
Calculate the Right Riemann Sum
55
Horizontal Washer Top axis values
(R and r)
R= axis-bottom
r= axis-top
f(x)=(4/t)-(1/6t3)+(8/t5)
Note: The variable "t" is on the bottom of the fraction, not to the side
f'(x)=-4t-2+(1/2)t-4-40t-6
INT(4x3-8x+7)dx
x4-4x2+7x+C
What formula is this?
[(y2-y1)/2](gap)+...
Riemann Sum: Trapezoid
x 1 2 3 4 5 6
y 5 7 9 11 13 15
Calculate the Middle Riemann Sum
36
Cross Section Area for Square
[INT(a,b)] s2
f(x)=(y5-5y3+2y)/y3
f'(x)=2(y4-2)/y3
INT[f(x)dx]= 10 INT[f(x)dx]= -20
[5,10] [0,15]
INT[f(x)dx]= -5
[10,15] What is [0,5]?
INT[f(x)dx]= -25
What rule/formula is this?
INT[a,c][f(x)dx]+INT[c,b][f(x)dx]=INT[a,b][f(x)dx]
Integral addition rule
x 1 2 3 4 5 6
y 5 7 9 11 13 15
Calculate the Trapezoid Riemann Sum
50
Cross section area of a semicircle
INT(a,b) [pi(r)2]/2
f(x)=(6/z3/2)+(1/8z4)-(1/3z10)
Note: The variable "t" is on the bottom of the fraction, not to the side
f'(x)=-9z-5/2-(1/2)z-5+(10/3)z-11
INT[x2(7+x3)2]
1/9(7+x3)3+C
What formula is this?
V'=4/3pi(r2)r'
Volume rate of change
x 0 3 6 9 12 15
y 5 7 9 11 13 15
Find the trapezoid sum
150
What does the "r" value represent in the "Area of a semicircle" formula?
r= top-bottom
(Hopefully you didnt overthink it)