How to evaluate the definite integral with trig and u substitution

The video tutorial explains the process of evaluating integrals using U-substitution. It begins with an introduction to the concept, followed by transforming integrals and derivatives. The tutorial then covers changing the bounds of integration when substituting variables and concludes with integrating and evaluating the function using the unit circle.

What is the derivative of U with respect to X if U is defined as 2X?

• 1

• 2

• X

• U

Why is it necessary to change the bounds of integration when substituting variables?

• To make the integral more complex

• To simplify the integral

• To match the new variable

• To avoid errors in calculation

What is the new upper bound for U when X is π/4?

• π/3

• π/2

• π/6

• π/4

What is the result of integrating the function in terms of U?

• Tangent of U

• Positive cosine of U

• Negative cosine of U

• Sine of U

What is the final result of the integration after evaluating the bounds?

• 1

• 0

• 1/2

• sqrt(3)/2