1,125 Answered Questions for the topic AP Calculus
. Find the volume of the solid obtained by rotating the area bounded by y=sin x and the x-axis on the interval 0= x= 2? about the x-axis.
a. 5.490 b. 2.754 c. 10.912 d. 9.870
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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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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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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
calculating area under curve
if you calculate the area under the curve f(x)=x2 from x=0 to x=5 using a left had rectangular approximation, a right hand approximation, and a midpoint rectangular approximation, in each case...
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integrating
when integrating ∫sin3xdx, a good first move would be to:
a) use u-substitution, letting u=sinx, and then integrating ∫u3du
b) use u-substitution, letting u=sin2x
c) rewrite the problem...
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dividing definite integrals
∫(top: b, bottom: a) ∫(f(x)/g(x))dx=(top: b, bottom: a)∫f(x)dx÷(top: b, bottom: a)∫g(x)dx
true or false?
definite integral
which of the following expressions are true about the definite integral of sinx on the interval [0,2Π]?
A) (top 2Π, bottom 0) ∫sinxdx= (Π →∞)lim (top: Π, bottom: i=0)∑sinxi 2Π
B) (top 2Π,...
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true or false?
y=e-x satisfies the differential equation, ( (d2y)/(dt2) )+y=0
true or false?
solution to differential equation
which of the following is a solution to the differential equation y''+2y'+y=0
a) y=cos2x
b) y=x2
c) y=xe-x
true or false?
y=sinx+cosx satisfies the differential equation ( (d2y)/(dt2) )+y=0
true or false?
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 is a solution of the differential equation dy/dx=y/x
a) y=2x
b) y=3x+2
c) y=ex
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solution of indefinite integral
What is a particular solution of the indefinite integral ∫(2)/(1-x2)dx that passes through (√3 , (Π/2)?
a) f(x)=√(3) tan-1x-(Π/6)
b) f(x)=2tan-1x-(Π/6)
c) f(x)=2tan-1x+√(3)
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find the general antiderivative of f(X)= 5/2x
a.) 5/2x2-C
b.) 5ln[2x]-C
c.) none of these
%MCEPASTEBIN%
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
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.)...
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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
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