Question

7.1 To solve ∫ ?? / (√7−?^(2)) by trig
substitution, we should set x = which of the following ?

x = sin θ x = 7 tan θ x = 7 sin θ

x = √7 sin θ x = 72 sin θ x = 7 sin2 θ

7.2 To use Integration by Parts with ∫e^(2x) x^(2) dx , we should
choose which ?

u = x and dv = ex dx u = e2x and dv = x2 dx

u = ex and dv = x2 dx u = x2 and dv = e2x dx

u = ex x and dv = ex x dx u = x and dv = e2x x
dx

7.3 To use Integration by Parts with ∫ ln x dx , we should choose
which ?

u = x and dv = ln dx u = x and dv = ln x dx

u = ln x and dv = dx u = 1 and dv = ln x dx

u = dx and dv = ln x u = ln x dx and dv = 1

Answer #1

integration of (x/(2x^2-4x-7))dx. Using trig. sub.

Question B:Consider the integral of sin(x) * cos(x) dx.
i) Do it using integration by parts; you might need the “break
out of the loop” trick. I would do u=sin(x), dv=cos(x)dx
ii) Do it using u-substitution. I would do u=cos(x)
iii) Do it using the identity sin(x)*cos(x)=0.5*sin(2x)
iv) Explain how your results in parts i,ii,iii relate to each
other.

To compute the integral ∫cos3(x)esin(x)dx, we should use first
the substitution u= __________ to obtain the integral ∫F(u)du,
where F(u)= __________ To compute the integral ∫F(u)du, we use the
method of integration by parts with
f(u)= __________ and g′(u)= __________ to get
∫F(u)du=G(u)−∫H(u)du , where G(u)= __________ and H(u)= __________
Now, to compute the integral ∫H(u)du, we need to use the method of
integration by parts a second time with f(u)= __________ and g′(u)=
__________ to get
∫H(u)du= __________ +C...

Answer the question, concerning the use of substitution in
integration.
If we use
u equals x squaredu=x2
as a substitution to find
Integral from nothing to nothing x e Superscript x squared
Baseline dx comma∫xex2 dx,
then which of the following would be a correct result?

Evaluate the integral: ∫8x^2 / √9−x^2 dx
(A) Which trig substitution is correct for this integral?
x=9sec(θ)
x=3tan(θ)
x=9tan(θ)
x=3sin(θ)
x=3sec(θ)
x=9sin(θ)
(B) Which integral do you obtain after substituting for x and
simplifying?
Note: to enter θθ, type the word theta.
(C) What is the value of the above integral in terms of θ?
(D) What is the value of the original integral in terms of x?

Evaluate the integral: ∫27√x^2−9 / x^4 dx
(A) Which trig substitution is correct for this integral?
x=3tan(θ)
x=27sin(θ)
x=3sin(θ)
x=9tan(θ)
x=3sec(θ)
x=9sec(θ)
(B) Which integral do you obtain after substituting for xx and
simplifying?
Note: to enter θθ, type the word theta.
(C) What is the value of the above integral in terms of θ?
(D) What is the value of the original integral in terms of x?

Important Instructions: (1) λ is typed as lambda. (2) Use
hyperbolic trig functions cosh(x) and sinh(x) instead of ex and
e−x. (3) Write the functions alphabetically, so that if the
solutions involve cos and sin, your answer would be
Acos(x)+Bsin(x). (4) For polynomials use arbitrary constants in
alphabetical order starting with highest power of x, for example,
Ax2+Bx. (5) Write differential equations with leading term
positive, so X′′−2X=0 rather than −X′′+2X=0. (6) Finally you need
to simplify arbitrary constants. For...

Important Instructions: (1) λ is typed as lambda. (2) Use
hyperbolic trig functions cosh(x) and sinh(x) instead of ex and
e−x. (3) Write the functions alphabetically, so that if the
solutions involve cos and sin, your answer would be
Acos(x)+Bsin(x). (4) For polynomials use arbitrary constants in
alphabetical order starting with highest power of x, for example,
Ax2+Bx. (5) Write differential equations with leading term
positive, so X′′−2X=0 rather than −X′′+2X=0. (6) Finally you need
to simplify arbitrary constants. For...

1. Al Einstein has a utility function that we can describe by
u(x1, x2) = x21 +
2x1x2 + x22
. Al’s wife, El Einstein, has a utility function v(x1,
x2) = x2 + x1.
(a) Calculate Al’s marginal rate of substitution between
x1 and x2.
(b) What is El’s marginal rate of substitution between
x1 and x2?
(c) Do Al’s and El’s utility functions u(x1,
x2) and v(x1, x2) represent the
same preferences?
(d) Is El’s utility function a...

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