U-Substitution and Integral Evaluation

The video tutorial explains how to evaluate a definite integral by analyzing the graph of the integrand, factoring, and using U-substitution. It demonstrates finding the antiderivative and evaluating the integral's limits. The tutorial concludes with verifying the results using a graphing calculator.

What does the definite integral of a non-negative function over a closed interval represent?

• The slope of the tangent line

• The length of the curve

• The area under the curve

• The volume of the solid

What is the first step in evaluating the given integral?

• Performing a U-substitution

• Using a graphing calculator

• Factoring out a constant from the numerator

• Changing the limits of integration

In the U-substitution method, what is U equal to?

• 9x^2

• x/3

• 3x

• 1 + 9x^2

What is the new limit of integration when x = 1/3 is substituted into U?

• 1/3

• 3

• 1

• 0

What is the anti-derivative of 1/(1 + u^2) with respect to u?

• 1/u

• ln|u|

• e^u

• arctan(u)

What angle in radians has a tangent function value of 1?

• π/6

• π/4

• π/3

• π/2

What is the final result of the definite integral in terms of π?

• π/4

• π/2

• π/6

• π/3

What is the decimal approximation of π/3?

• 1.5708

• 0.7854

• 1.0472

• 2.0944

What mode should the graphing calculator be in to verify the result?

• Degree mode

• Graph mode

• Radian mode

• Scientific mode

Which function on the calculator is used to enter the definite integral?

• Option 3 for matrix operations

• Option 9 for function integration

• Option 5 for differentiation

• Option 7 for summation