Question

Which change of variables is suggested by the integral containing √(100 - x^2)?

A) u=x+10
B) u=√(100−x²)
C) u=x⁄10
D) u=cos^(-1)(x⁄10)

Answer 1

The suggested change of variables for the integral containing √(100 - x^2) is u=√(100−x²).

Step-by-step explanation:

The suggested change of variables for the integral containing √(100 - x^2) is option B) u=√(100−x²).

We can see that the integral contains the expression √(100 - x^2), which is the form of a standard trigonometric function, specifically the equation of a circle centered at the origin with a radius of 10 units. So, it makes sense to use a change of variables that simplifies this expression to a standard trigonometric function, such as u=√(100−x²).

By substituting u=√(100−x²), we can rewrite the integral in terms of u and evaluate it using trigonometric techniques.