Definite Integration and Completing the Square

This video tutorial covers integration involving inverse trigonometric functions, focusing on definite integration and completing the square. It provides a detailed analysis of two integrals, using trigonometric identities and differentiation rules to solve them. The video also includes practical examples and calculations, emphasizing the importance of recognizing derivative forms to simplify integration problems.

What is the main focus of this video tutorial?

• Graphing polynomial functions

• Definite integration and completing the square

• Differentiation of trigonometric functions

• Solving linear equations

What is the first step in completing the square for the expression x^2 - 6x?

• Take half of the coefficient of x and square it

• Multiply by 2

• Add 6 to both sides

• Subtract 9 from both sides

After completing the square, what is the expression x^2 - 6x + 9 equivalent to?

• (x + 6)^2

• (x - 6)^2

• (x + 3)^2

• (x - 3)^2

What is the value of 'a' when a^2 = 4 in the context of the integration problem?

• 3

• 2

• 4

• 1

How do you evaluate the definite integral from 2 to 4 of the function using the arc tangent?

• By multiplying the limits

• By adding the limits

• By finding the difference of arc tangent values at the limits

• By dividing the limits

What is the derivative of arc sine x?

• 1 over x squared

• x squared over 1 minus x

• 1 over the square root of 1 minus x squared

• x over the square root of 1 minus x squared

What substitution is used to simplify the integration of arc sine x?

• u = x - 3

• u = x^2

• u = 1/x

• u = arc sine x

What is the result of evaluating the integral of arc sine x from 0 to sqrt(3)/2?

• pi divided by 3

• pi squared divided by 18

• pi divided by 6

• pi squared divided by 9

What is the significance of the result pi squared over 18 in the context of the function's graph?

• It represents the area under the curve

• It is the maximum value of the function

• It is the x-intercept of the function

• It is the slope of the tangent line

What is the angle in radians for arc sine of sqrt(3)/2?

• pi/4

• pi/3

• pi/2

• pi/6