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Integral operator is a(n) _______ operator
area

Given: g(x) = intg{ f(x) dx }. The constant of integration is _____ g(x)
independent of

Given: g(x) = intg{ f(x) dx }. The first value of g(x) must include an external value (or number), which is called the constant of integration.
true

Given: g(x) = intg{ f(x) dx }. The first value of g(x)
 cannot be determined from g(x) = intg{ f(x) dx }
 must be given in addition to g(x) = intg{ f(x) dx }
 both of these

Given: g(x) = intg{ f(x) dx }. The intg_a_b{ f(x) dx } is the change in ___ between x=a and x=b.
g(x)

Y = intg_a_b{ f(x) dx }. Y is a
number

Y = intg_a_b{ f(x) dx }. If Y is negative, then f(x) was primarily _____ the x axis.
below

Y = intg_a_b{ f(x) dx }. If Y is positive, then f(x) was primarily _____ the x axis.
above

Y = intg_a_b{ f(x) dx }. Area above or below f(x) means
area between the function and the x axis

Y = intg_a_b{ f(x) dx }. Y is the area _____ between x=a and x=b.
above f(x) or below f(x)

intg_a_b{ f(x) dx }, is known as a(n)
definite integral

In Y = intg_a_b{ f(x) dx }. Y is
a number, which is the area bounded by the function and the x axis

In intg_a_b{ f(x) dx }, b is the _____ limit of integration.
upper

In intg_a_b{ f(x) dx }, a is the _____ limit of integration.
lower`

In intg_a_b{ f(x) dx }, the limits of integration are x=
a and b

In intg{ f(x) dx }, f(x) is a function. Can f(x) have a constant value?
yes

In intg{ f(x) dx }, the independent variable is
x

intg{ f(x) dx } means integral of the function f(x) with respect to x.
true

The definite integral of a function is
number

Integral operator is a(n) _______ operator
area

The indefinite integral of a function is
a function

The definite integral of a function is
area (a number) under/over the function

The integral of a constant is
not defined

One way to remember which axis is the abscissa and ordinate is the shape of the mouth when saying the words.
true



h=cos x; intg{ h dx } = ______ at x=pi/2 if C=2.
3

h=cos x; intg{ h dx } = ______ at x=pi/2 if C=1.
2

h=cos x; intg{ h dx } = ______ at x=pi/2 if C=0
1







The relationship indicated in fig 9060B is
dL^2 = dx^2 + dy^2

Differential area in fig 9060C is
y*dx

The surface area indicated in fig 9060D is formed by rotating ____ about the ___ axis
y(x), x

Fig 9060E shows the differential area dA =
2*pi*y*dL

Fig 9060F shows the differential volume dV =
pi*y^2*dx

The volume indicated in fig 9060D is formed by rotating ____ about the ___ axis.
y(x), x

Fig 9060E shows the differential area dA =
2*pi*y*dL

The relationship indicated in fig 9060B is
dL^2 = dx^2 + dy^2

Differential length in fig 9060A is
dL

The volume of a y(x) with apex at the origin is V = integ{ dV } and dV= pi*y^2*dx which is a differential volume of a ______ in Fig9060F.
cylinder

The surface area of any y(x) rotated about the x axis with apex at the origin is A = integ{ dA }, where dA=______ in Fig9060E.
2*pi*y*dL

The surface area of a cone with apex at the origin and cone axis is along the xaxis is A = integ{ dA } and dA=
2*pi*y*dL

If the function y(x) is rotated about the x axis in Fig9060D, then ________ is generated.
an enclosed volume and surface area

If the function y(x)=2x is rotated about the x axis, then ________ is generated for positive x.
cone

If the function y(x)=3x^2 is rotated about the x axis, then ________ is generated for positive x.
a horn

A=intg{dA} means integrate over all differential areas or addup all the area segments, where dA=y*dx in Fig9060C. Classical integration (vs numerical integration) is possible when the function y(x) is known.
true

A=intg{dA} means integrate over all differential areas or addup all the area segments, and dA=y*dx where dx in Fig9060C means
rectangle width

A=intg{dA} means integrate over all differential areas or addup all the area segments, and dA=y*dx where y in Fig9060C means
distance from the xaxis to the function y(x) in the y direction

A=intg{dA} means integrate over all differential areas or addup all the area segments, where dA=y*dx in Fig9060C is the area of a
rectangle of height y and width dx

A=intg{dA} means integrate over all differential areas or addup all the area segments, where A means
area

A=intg{dA} means integrate over all differential areas or addup all the area segments, where dA means
 all of these
 differential area
 delta area
 smallestpossible area segment

Draw the right triangle: dx along the x axis; dy along the y axis; and dL along the hypotenuse. Write the pythagorean equation in Fig9060B. Divide by dx^2. dL=
sqrt(1+y'*y')*dx

L=intg{dL} means integrate over all differential lengths or addup all the length segments, where dL= ______ using Fig9060B.
sqrt(1+y'*y')*dx

L=intg{dL} means integrate over all differential lengths or addup all the length segments, where L means total
length

L=intg{dL} means integrate over all differential lengths or addup all the length segments, where dL in Fig9060A means
 all of these
 differential length
 delta length
 smallestpossible length segment

In a righthand coordinate system,
ixj = k

2. A function that produces a 3D surface is z(x,y), which means that z is a function of
x and y

3. The number of slopes for any point on a 3D surface is
infinite

4. When one takes a derivative of a 3D surface, the direction of the derivative
must also be specified

The derivative of z(x,y) with y held constant is the ____ derivative of z with respect to ____.
partial, x

The derivative of z(x,y) with x held constant is the ____ derivative of z with respect to ____.
partial, y

Partial derivatives are meaningful for 3D surfaces
true

Partial derivative of z(x,y) with respect to x is the same a regular derivative except ___ is considered constant.
y

Partial derivative of z(x,y) with respect to y is the same a regular derivative except ___ is considered constant.
x

The number of tangent planes for any point on a 3D surface is
one

The number of tangent lines for any point on a surface is
infinite

The number of lines that define a plane is
two

z(x,y) = f(x,y). A common notation of partial derivative of f with respect to x is
fx

z(x,y) = f(x,y). A common notation of partial derivative of f with respect to y is
fy

The derivative of z(x,y) can be the partial derivative of z with respect to x, because ___ is held constant.
y

The derivative of z(x,y) can be the partial derivative of z with respect to y, because ___ is held constant.
x

. Engineers often encounter laboratory data (x0,y0; x1,y1; ... xn,yn), where y is a function of x. The function y that passes exactly through all the data points ____ wellknown standard function.
will probably not match any

Laboratory data (x,y pairs of numbers) might reflect some wellknown standard function, but will never match exactly because of
all of these

Laboratory data (x,y pairs of numbers) can be numerically integrated (approximated) by
 all of these and many others
 Simpson's method
 backward integration
 forward integration
 trapezoidal integration

Forward integration is the area of
rectangles

Backward integration is the area of
rectangles

Trapezoidal integration is the area of
trapezoids

Simpson's integration is the area under
parabolas

The average of forward and backward integration is ____ integration.
trapezoidal

(y0/2 + y1 + y2 + ... + yn/2)*deltax is the formula for _____ integration.
trapezoidal

(y1 + y2 + ... + yn)*deltax is the formula for ______ integration. Note the first point (y0) is not used.
backward

(y0 + y1 + ... + y(n1))*deltax is the formula for ______ integration. Note the last point (yn) is not used.
forward

(2*sum_of_all_y's  y0/2 yn/2)*deltax is the formula for _____ integration. Add all the y's; multiply by 2; subtract half the first and last; multiply by deltax.
trapezoidal

(y0+4y1+2y2+4y3+2y4+...+2y(n2)+4y(n1)+yn)*deltax/3 is the formula for ____ integration.
Simpson's

The number of data points permitted in Simpson's integration is
odd (n=even)

The number of data points permitted in trapezoidal integration is
either odd or even

The number of data points permitted in backward or forward integration is
either odd or even

Numerical integration can be implemented with forward, backward, trapezoidal, and Simpson's integration in any computer or calculator.
true

Numerical integration can be implemented with MS Excel using forward, backward, trapezoidal, and Simpson's integration. The most difficult would be:
Simpson's

Engineers often encounter laboratory data (x0,y0; x1,y1; ... xn,yn), where y is a function of x. Any one of the standard functions can be forced to approximate the data.
true

The feature in Excel called ____ can be used to force a standard function to approximate any set of laboratory data (x0,y0; x1,y1; ... xn,yn).
trend line

Start to add a trendline to an Excel graph by
clicking on one of the data points

