Question

Evaluate the integral: $\int \frac{16x^2}{\sqrt{9 - x^2}} dx$ (A) Which trig substitution is correct for this integral? $x = 3 \sec(\theta)$ $x = 3 \tan(\theta)$ $x = 9 \sec(\theta)$ $x = 3 \sin(\theta)$ $x = 9 \tan(\theta)$ $x = 9 \sin(\theta)$ (B) Which integral do you obtain after substituting for $x$ and simplifying? Note: to enter $\theta$, type the word theta. $\int \text{ } d\theta$ (C) What is the value of the above integral in terms of $\theta$? + C (D) What is the value of the original integral in terms of $x$? $72 \arcsin(\frac{1}{3}x) - 36 \sin(2 \arcsin(\frac{1}{3}x))$ + C

          Evaluate the integral: $\int \frac{16x^2}{\sqrt{9 - x^2}} dx$
(A) Which trig substitution is correct for this integral?
$x = 3 \sec(\theta)$
$x = 3 \tan(\theta)$
$x = 9 \sec(\theta)$
$x = 3 \sin(\theta)$
$x = 9 \tan(\theta)$
$x = 9 \sin(\theta)$
(B) Which integral do you obtain after substituting for $x$ and simplifying?
Note: to enter $\theta$, type the word theta.
$\int \text{ } d\theta$
(C) What is the value of the above integral in terms of $\theta$?
+ C
(D) What is the value of the original integral in terms of $x$?
$72 \arcsin(\frac{1}{3}x) - 36 \sin(2 \arcsin(\frac{1}{3}x))$
+ C

Evaluate the integral: ∫(16x^2)/(√(9 - x^2)) dx
(A) Which trig substitution is correct for this integral?
x = 3 sec(θ)
x = 3 tan(θ)
x = 9 sec(θ)
x = 3 sin(θ)
x = 9 tan(θ)
x = 9 sin(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?
72 arcsin((1)/(3)x) - 36 sin(2 arcsin((1)/(3)x))
+ C

Added by Dorothy M.

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