Final answer:
To evaluate the integral √(x² - 144), it is suggested to use a change of variables. Let x = 12sinh(t) and find dx in terms of dt. Substitute x and dx in the integral with the new variables and simplify the integral to evaluate it.
Step-by-step explanation:
To evaluate an integral containing √(x² - 144), it is suggested to use a change of variables. In this case, we can let x = 12sinh(t). This change of variables simplifies the integral and allows us to solve it more easily.
First, let's find dx in terms of dt:
dx = 12cosh(t)dt
Next, let's express x² - 144 in terms of t:
x² - 144 = (12sinh(t))² - 144 = 144sinh²(t) - 144 = 144(sinh²(t) - 1)
Now, substitute x and dx in the integral with the new variables:
∫ √(x² - 144) dx = ∫ √(144(sinh²(t) - 1)) 12cosh(t) dt
Once this substitution is made, you can simplify the integral and evaluate it accordingly.