Question

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?

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: ∫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

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 following integral using trigonometric
substitution.. ∫dx/(x²√(16x²-9)), x＞3/4
an exact answer

Evaluate the line integral of " (y^2)dx +
(x^2)dy " over the closed curve C which is the triangle
bounded by x = 0, x+y = 1, y = 0.

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