Question

what change of variables is suggested by an integral containing $sqrt{x^{2}+196}$?
choose the correct answer below.
a. $x = 14sin\theta$
b. $x = 196\tan\theta$
c. $x = 196sin\theta$
d. $x = 14\tan\theta$

Explanation:

Step1: Recall trig - substitution rule

For $\sqrt{x^{2}+a^{2}}$, we use $x = a\tan\theta$. Here $a^{2}=196$, so $a = 14$.

Step2: Determine the substitution

The substitution for $\sqrt{x^{2}+196}$ is $x = 14\tan\theta$.

Answer:

D. $x = 14\tan\theta$