Integration of Absolute Value of X

The video tutorial explains how to integrate the absolute value of X function. It begins with graphing the function, showing that it can be divided into two parts: positive X for X greater than or equal to zero, and negative X for X less than zero. The tutorial then demonstrates how to integrate each part separately using the power rule, resulting in two antiderivatives: 1/2 x squared plus C for X greater than or equal to zero, and negative 1/2 x squared plus C for X less than zero. The video concludes with the final integration result.

What does the graph of the absolute value of x look like?

• A V-shaped graph

• A parabola

• A straight line through the origin

• A circle

How is the absolute value function divided for integration?

• Into three parts

• Into two parts: x >= 0 and x < 0

• Into four parts

• Into a single part

What is the integral of x when x is greater than or equal to zero?

• x^2 + C

• 1/2 x^2 + C

• x^3/3 + C

• x + C

What is the integral of -x when x is less than zero?

• -x^3/3 + C

• -x + C

• -1/2 x^2 + C

• -x^2 + C

Which rule is used to find the antiderivative of x?

• Quotient Rule

• Product Rule

• Chain Rule

• Power Rule

What is the final expression for the integral of the absolute value of x?

• x^3/3 + C

• x + C

• 1/2 x^2 + C for x >= 0 and -1/2 x^2 + C for x < 0

• x^2 + C