Question

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

Answer #1

ALL THE BEST....!!

1. Find the antiderivative: indefinite integral(
sec^2(sqrt(x)dx
(a) State substitution. Use w for new variable
(b) Write new integral
(c) Write first step in solving new integral
(d) Write antiderivative answer
2. definite integral from 0 --> 1 (y + 1) / (e^(3y)) dy Leave
answer in exact form but simplify as much as possible
(a) Write problem in form so that integration by parts
applies.
(b) Write next step in solving integral
(c) Write answer in exact form

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: ∫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?

(#9) evaluate integral SQRT(16x^2-1)dx using trigonometric
substitution

Integrate xsqrt(36-(x-6)^2)dx. Using trig. substitution.

Integrate (x^3)*sqrt(x^2 +4) dx, using trigonometric
substitution.

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

Use the definition of the definite integral to evaluate Integral
from 2 to 6 left parenthesis x squared minus 4 right parenthesis
dx.

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

Evaluate definite integral (0 to pi/2) secxtanx-sec^2(x) dx

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