Question

Evaluate the integral: ∫23√x2−4x4dx

(A) Which trig substitution is correct for this integral?

- x=4sec(θ)
- x=4tan(θ)
- x=23sin(θ)
- x=2sec(θ)
- x=2tan(θ)
- x=2sin(θ)

(B) Which integral do you obtain after substituting for x and
simplifying?

Note: to enter θ, type the word theta.

∫ dθ

(C) What is the value of the above integral in terms of θ?

+ C

(D) What is the value of the original integral in terms of x?

+ C

Answer #1

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?

Evaluate the integral using trig substitution.
definite integral from 1 to sqrt(2) 6 / (x^2 sqrt(4-x^2))dx
(a) write the definition for x using the triangle
(b) write the new integral before any simplification
(c) write the new integral after simplifying and in the form ready
to integrate
(d) write the solution in simplified exact form
write all answers next to the specified letter above

After an appropriate trig substitution, the integral
x^2sqrt(4-x^2)
dx
is equivalent to which of the following?

Evaluate the integral using the indicated trigonometric
substitution. (Use C for the constant of integration.)
x3
x2 + 16
dx
, x = 4
tan(θ)

In this exercise, you will analyze the supply-demand equilibrium
of a city under some special simplifying assumptions about land
use. The assumptions are: (i) all dwellings must contain exactly
1,500 square feet of floor space, regardless of location, and (ii)
apartment complexes must contain exactly 15,000 square feet of
floor space per square block of land area. These land-use
restrictions, which are imposed by a zoning authority, mean that
dwelling sizes and building heights do not vary with distance to...

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