Question

Evaluate the integral: $int frac{12}{x^{2} sqrt{x^{2}+16}} d x$ (A) Which trig substitution is correct for this integral? $x=4 an ( heta)$ $x=12 sec ( heta)$ $x=4 sin ( heta)$ $x=16 sin ( heta)$ $x=16 sec ( heta)$ $x=16 an ( heta)$ (B) Which integral do you obtain after substituting for $x$ and simplifying? Note: to enter $ heta$, type the word theta. $int$ [ ] $d heta$ (C) What is the value of the above integral in terms of $ heta$ ? [ ] $+C$ (D) What is the value of the original integral in terms of $x$ ? [ ] $+C$

          Evaluate the integral: $int frac{12}{x^{2} sqrt{x^{2}+16}} d x$

(A) Which trig substitution is correct for this integral?
$x=4 	an (	heta)$
$x=12 sec (	heta)$
$x=4 sin (	heta)$
$x=16 sin (	heta)$
$x=16 sec (	heta)$
$x=16 	an (	heta)$

(B) Which integral do you obtain after substituting for $x$ and simplifying?
Note: to enter $	heta$, type the word theta.
$int$ [ ] $d 	heta$

(C) What is the value of the above integral in terms of $	heta$ ?
[ ] $+C$

(D) What is the value of the original integral in terms of $x$ ?
[ ] $+C$

$Evaluate the integral: int frac12x^2 sqrtx^2+16 d x (A) Which trig substitution is correct for this integral? x=4 an ( heta) x=12 sec ( heta) x=4 sin ( heta) x=16 sin ( heta) x=16 sec ( heta) x=16 an ( heta) (B) Which integral do you obtain after substituting for x and simplifying? Note: to enter heta, type the word theta. int [ ] d heta (C) What is the value of the above integral in terms of heta ? [ ] +C (D) What is the value of the original integral in terms of x ? [ ] +C$

Added by Monét T.

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