Integrals
Represents the constant of integration
What is C
The instantaneous rate of change at a point is equal to the slope of the this line at that point
What is tangent
Which function is on top: y=x or y=x2-2
What is y=x
No matter what shape you revolve, the cross-section will be this
What is a circle
An equation where one variable is written in terms of another
What is explicit form
The integral of 3x dx
What is 3x2/2 +C
The derivative of f(x)=(3x-2)2
What is f'(x)=6(3x-2)
Which is on top: f(x) = ln x or g(x) = (x-2)2-3
What is f(x)=ln x
Washer or Disk
y=x2+3 , y=1 , x=0 , x=1
What is Washer
Any horizontal or vertical line that a solid revolves around
The integral of 3x4-5x2+x dx
What is 3x5/5 - 5x3/3 + x2/2 + C
The derivative of f(x) = 1/4 x4 - 8x2
What is f'(x)= x(x2-16)
Find the area of the region between y = x2-3x-4 and the x-axis
What is 125/6
Washer or Disk
x=-y2+5 , y=1 , x=0 , y=0
Comparing different choices to determine which might be "efficient"
What is optimization
The definite integral of 4x3+6x2+4x dx
What is f(x)= x4+2x3+2x2+C
Using the chain rule, find the derivative of f(x) = (2x3 + 1)2
What is 24x5+12x2
The direction of the bounds when the area is with respect to the x-axis
What is vertical
The integral of area is this
What is volume
The difference between the values of the integral at specified upper and lower bounds
What is definite integral
Find the integral between 1 and 0 (4x+1) dx
y = (x+5)2, find y'(0)
What is 10
Use a calculator to find the area: The integral between 3 and 1 ln3x - lnx dx
What is 2.1972
A solid generated by revolving a plane about a line
Points on the graph where it changes from increasing to decreasing or vice versa
What is relative extrema