bc calc: integrals as net change
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18 Terms
distance traveled =
ā« |velocity function|
average speed =
total distance traveled / change in time
average velocity =
displacement / change in time
net change in velocity =
ā« acceleration function
new position =
old position + ā« displacement function
new velocity =
old velocity + ā« acceleration function [net change in velocity]
when is particle moving right, moving left, stopped, changing direction, etc
right = pos. velocity
left = neg. velocity
stopped = when vel. equals 0
change directions = when vel. changes sign
when is the speed of the particle increasing or decreasing and why
increases = vel. and acc. have same sign
decreases = vel. and acc. habe opposite signs
volume of square
ā« sĀ²dx
volume of rectangle
ā« h*sĀ²dx
volume of equilateral triangles
ā« (sqrt3/4)*sĀ²dx
volume of isosceles right triangle with a leg in xy plane
ā« sĀ²/2 dx
volume of isosceles right triangle with the hypotenuse in the xy plane
ā« sĀ²/4 dx
volume of semicircle
ā« pi/8 * sĀ²
volume by disks
ā« pi * rĀ² dx (*radius perp to AOR)
position at t
x(t) = x(t1) + ā«[t1āt] v(t)
displacement of object
ā«[t1 ā t2] v(t)dt = x(t2) - x(t1)