Integration Techniques and Properties

Integration Techniques and Properties

Assessment

Interactive Video

Created by

Liam Anderson

Mathematics

11th Grade - University

Hard

04:37

This video tutorial explains how to evaluate a definite integral using the method of u-substitution. It begins by analyzing the integrand function and setting up the substitution by letting the denominator be equal to u. The tutorial then walks through the process of substituting and simplifying the integral, finding new limits of integration, and evaluating the integral to find the result. Finally, it provides a graphical interpretation of the integral over a specified interval.

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10 questions

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1.

MULTIPLE CHOICE

30 sec • 1 pt

What is the degree of the polynomial in the denominator of the integrand function?

2.

MULTIPLE CHOICE

30 sec • 1 pt

Why do we let the denominator equal u in the substitution method?

3.

MULTIPLE CHOICE

30 sec • 1 pt

What is the expression for du after differentiating the denominator?

4.

MULTIPLE CHOICE

30 sec • 1 pt

What is the new lower limit of integration for u when x equals 1?

5.

MULTIPLE CHOICE

30 sec • 1 pt

What is the new upper limit of integration for u when x equals 4?

6.

MULTIPLE CHOICE

30 sec • 1 pt

What is the anti-derivative of 1/u with respect to u?

7.

MULTIPLE CHOICE

30 sec • 1 pt

How do we simplify the expression ln(60) - ln(21) using logarithm properties?

8.

MULTIPLE CHOICE

30 sec • 1 pt

What is the approximate value of the definite integral to four decimal places?

9.

MULTIPLE CHOICE

30 sec • 1 pt

What does the green shaded region on the graph represent?

10.

MULTIPLE CHOICE

30 sec • 1 pt

What does the value of the definite integral indicate about the shaded region?

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