77 Answered Questions for the topic AP Calc
Given a solid whose cross-section is defined by A(x), the volume of the solid is given by _____________________.
a) V=∫A'(x)dx
b) V=∫A(x)dx
c) V=Π∫A(x)dx
d)none of these
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08/18/15
Which of the following gives the volume of the solid created by revolving a curve f(x) around the y-axis?
V=2Π∫ xf(x)dx
V=Π∫ xf(x)dx
V=2Πx2f(x)dx
V=Π2∫ xf(x)dx
looking at a velocity time graph
when looking at a velocity vs. time graph, how can one determine the total distance traveled as well as the displacement?
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net change
the net change in y=f(x), as x changes from a to b is given by___________.
∫abs(F'(x)) dx
∫F'(x) dx
∫ abs(F(x)) dx
∫F(x) dx
none of these
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08/16/15
TRUE OR FALSE?
if f(x) is an even function,(above integral sign: 0 below integral sign: -a) ∫f(x)dx= (above integral sign: a below integral sign: 0) -∫f(x)dx true or false?
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which of the following integrals is INCORRECT?...
A) ∫tanxdx=sec2x+C
B) ∫cscxdx=ln[cscx-cotx]+C
C) ∫cotxdx=ln[sinx]+C
true or false?
if f(x) is an even function,
(above integral sign: 0 below integral sign: -a) ∫f(x)dx= (above integral sign: a below integral sign: 0) -∫f(x)dx
true or false?
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u-substitution
When integrating ∫esinxcosdx, a good choice to use for your u-substitution would be which of the following:
a) u=cosxb) u=sinx
c) u=esinx
08/15/15
find the general antiderivative of f(X)= 5/2x
a.) 5/2x2-C
b.) 5ln[2x]-C
c.) none of these
%MCEPASTEBIN%
08/14/15
solving integral
∫ ( t/(√(2t2-1) )dt=________
A) (-1/2)(√(2t2-1))+C
B) 4(√(2t2-1))+C
C) 8(√(2t2-1)+C
D) -( (1)/(4(2t2-1)) )+C
E) (1/2)(√(2t2-1))+C
08/13/15
substituting in an integral
If the substitution √(X)=sin y is made in the integrand of:
(top of the integral sign is (1/2), bottom of the sign is 0) ∫ ( √(X) )/( √(1-X) )dx, the resulting integral is_____________.
A.)...
more
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08/12/15
solving integrals
∫( (du)/(u(u2-1)1/2) ) = __________________
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08/12/15
chain rule is also know as
The Chain Rule for antiderivatives is also known as the ___________________ rule.
-derivative
-substitution
-product
-integral
08/12/15
find area under curve
Using the left-had approximation method with 5 equal subintervals, find the area under the curve f(x)=√(1+x3) on the interval [0,1].
a.) 1.074
b.) 1.156
c.) 2.356
d.) 1.110
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08/12/15
solving using integrals
if I have a graph of f(x) and I want to find (on the top of the integral sign is 5, and on the bottom is -2) ∫f(x)dx
what would ∫f(x)dx equal?... (if the graph has points at (-5,2) (-2,0)...
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08/12/15
solving integrals
∫ ( (dx)/√(x2+36) )=_____________
a. ( (√(x2+36)+x)/6 )+C
b. ln abs( (x+6)/(√(x2+36)) )+C
c. ln ( (√(x2+36)+x)/6 )+C
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08/12/15
trigonometric substitution to evaluate integral
Which trigonometric substitution can be used to evaluate the integral: ∫ ( (dx)/(√(a2+x2)) ) ...?
x= a tanθ
x=a sinθ
x=a secθ
08/12/15
what is the antiderivative?
what would be the antiderivative of f(x)=12x3-9x2+8x-3
I believe it would be 3x4-3x3+4x2-3x+7 , is that correct?
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08/12/15
second derivatives
Using the second order derivative equation: ( (d2y)/(dx2) )-9y=o
Which of the following would be true?
y= e3x
y=e-3x
y=2e-3x
y=xe3x
11/23/14
double derivative y^3-xy=5 PLEASE HELP!!!
i just cant get why i got this wrong and i cant find the answer online, please tell me the answer and how to do this step by step, thank you so much!!
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lim of (1-cos5x)/(cos6x-1) as x->0
lim of (1-cos5x)/(cos6x-1) as x->0
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