Reading...
Play button
Play button
Use LEFT and RIGHT arrow keys to navigate between flashcards;
Use UP and DOWN arrow keys to flip the card;
H to show hint;
A reads text to speech;
29 Cards in this Set
- Front
- Back
|
Integral of 0 to 8 dx/sqrt(1+x) =
------------------------ 1 3/2 2 4 6 |
4
|
|
|
The region bounded by the x-axis and the part of the graph of y = cos x between x = -pi/2 and x=pi/2 is separated into two regions by the line x = k. If the area of the region for -pi/2 <= x <= k is three times the area of the region for k <= x <= pi/2 then k =
--------------------------- arcsin(1/4) arcsin(1/3) pi/6 pi/4 pi/3 |
pi/6
|
|
|
integral of 0 to 1 sqrt(x^2-2x+1) dx is
----------------------- -1 -1/2 1/2 1 none of the above |
1/2
|
|
|
integral of 0 to 1 (4-x^2)^-3/2 dx =
-------------------- 2-sqrt(3)/3 2sqrt(3)-3/4 sqrt(3)/12 sqrt(3)/3 sqrt(3)/2 |
2-sqrt(3)/3
|
|
|
If f(x) = (x^2+1)^(2-3x), then f'(1) =
------------- -1/2ln(8e) -ln(8e) -3/2ln(2) -1/2 1/8 |
-3/2ln(2)
|
|
|
If n is a non-negative integer, then integral from 0 to 1 x^n dx = integral 0 to 1 (1-x)^n dx for
----------------------- no n n even, only n odd, only nonzero n, only all n |
all n
|
|
|
integral sin(2x+3) dx =
----------------- 1/2cos(2x+3)+C cos(2x+3)+C -cos(2x+3)+C -1/2cos(2x+3)+C -1/5cos(2x+3)+C |
-1/2cos(2x+3)+C
|
|
|
Integral (x^3-3x) dx =
---------------- 3x^2-3+C 4x^4-6x^2+C x^4/3 - 3x^2+C x^4/4 - 3x+C x^4 - 3x^2/2+C |
x^4/4 - 3x^2/2 +C
|
|
|
A particle moves in a straight line with velocity v(t) = t^2. How far does the particle move between times t = 1 and t = 2?
------------------ 1/3 7/3 3 7 8 |
7/3
|
|
|
The acceleration alpha of a body moving in a straight line is given in terms of time t by alpha = 8-6t. If the velocity of the body is 25 at t=1 and if s(t) is the distance of the body from the origin at time t, what is s(4) - s(2)?
-------------------------------- 20 24 28 32 42 |
32
|
|
|
The area of the region bounded by the lines x = 0, x = 2, and y = 0 and the curve y = e^x/2 is
--------------------- e-1/2 e-1 2(e-1) 2e-1 2e |
2(e-1)
|
|
|
If F and f are continuous functions such that F'(x)=f(x) for all x, then integral a to b f(x) dx is
--------------- F'(a) - F'(b) F'(b) - F'(a) F(a) - F(b) F(b) - F(a) none of the above |
F(b) - F(a)
|
|
|
integral of 0 to 1 (x+1) e^x+2+2x dx =
------------------- e^3/2 (e^3-1)/2 (e^4-e)/2 e^3 - 1 e^4 - e |
(e^3-1)/2
|
|
|
integral 0 to pi/4 tan^2x dx =
------------------- (pi/4) -1 1 - (pi/4) 1/3 sqrt(2) - 1 (pi/4) + 1 |
1 - (pi/4)
|
|
|
Integral 0 to 1/2 2x/sqrt(1-x^2) dx =
----------------- 1- (sqrt(3)/2) 1/2ln3/4 pi/6 pi/6 - 1 2 - sqrt(3) |
2 - sqrt(3)
|
|
|
Integral 1 to 2 x-4/x^2 dx =
-------------------- -1/2 ln 2 - 2 ln 2 2 ln 2 + 2 |
ln 2 - 2
|
|
|
integral 5/1+x^2 dx =
------------------------ -10x / (1+x^2) +C 5/2x ln(1+x^2)+C 5x - 5/x +C 5 arctan x + C 5 ln (1+x^2) + C |
5 arctan x + C
|
|
|
If integral 1 to 2 f(x-c) dx = 5 where c is a constant, then integral 1-c to 2-c f(x) dx =
------------------------ 5 + c 5 5 - c c - 5 -5 |
5
|
|
|
integral 1 to 2 x^-3 dx =
----------------- -7/8 -3/4 15/64 3/8 15/16 |
3/8
|
|
|
If integral -1 to 1 e^-x^2 dx = k, then integral -1 to 0 e^-x^2 dx =
---------------- -2k -k -k/2 k/2 2k |
k/2
|
|
|
The velocity of a particle moving on a line at time t is v = 3t^1/2 + 5t^3/2 meters per second. How many meters did the particle travel from t = 0 to t = 4?
------------------ 32 40 64 80 184 |
80
|
|
|
integral 1 to 2 x^2 -1/x+1 dx =
------------------ 1/2 1 2 5/2 ln 3 |
1/2
|
|
|
If integral -2 to 2 (x^7 + k) dx = 16, then k =
------------------ -12 -4 0 4 12 |
4
|
|
|
Integral 0 to 3 |x-1| dx =
------------------- 0 3/2 2 5/2 6 |
5/2
|
|
|
integral tan(2x) dx =
------------- -2 ln |cos(2x)| + C -1/2 ln|cos(2x)| + C 1/2 ln|cos(2x)|+C 2 ln |cos(2x)| + C 1/2 sec(2x)tan(2x) + C |
-1/2 ln|cos(2x)| +C
|
|
|
integral 0 to pi/3 sin(3x) dx =
---------------- -2 -2/3 0 2/3 2 |
2/3
|
|
|
d/dx integral 2 to x sqrt(1+t^2) dt =
--------------------- x/sqrt(1+x^2) sqrt(1+x^2) -5 sqrt(1+x^2) x/sqrt(1+x^2) - 1/sqrt(5) 1/2sqrt(1+x^2) - 1/2sqrt(5) |
sqrt(1+x^2)
|
|
|
A particle with velocity at any time t given by v(t) = e^t moves in a straight line. How far does the particle move from t = 0 to t = 2?
--------------- e^2 - 1 e - 1 2e e^2 e^3/3 |
e^2 -1
|
|
|
integral sec ^2 x dx =
------------- tan x + C csc ^2 x + C cos^2 x + C sec^3 x/3 + C 2sec^2xtanx + C |
tanx + C
|
