Question

what change of variables is suggested by an integral containing $sqrt{x^{2}-484}$? choose the correct answer. a. $x = 22sec\theta$ b. $x = 22\tan\theta$ c. $x = 484sec\theta$ d. $x = 22sin\theta$

Explanation:

Step1: Recall trig - substitution rule

For $\sqrt{x^{2}-a^{2}}$, the substitution $x = a\sec\theta$ is used.

Step2: Identify the value of $a$

Given $\sqrt{x^{2}-484}$, since $484 = 22^{2}$, then $a = 22$.

Step3: Determine the substitution

The substitution for $\sqrt{x^{2}-484}$ is $x=22\sec\theta$.

Answer:

A. $x = 22\sec\theta$