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Integrals Involving Trigonometric Substitutions

Integrals Involving Trigonometric Substitutions

Assessment

Interactive Video

Mathematics

10th - 12th Grade

Practice Problem

Hard

CCSS
HSF.TF.C.8

Standards-aligned

Created by

Amelia Wright

FREE Resource

Standards-aligned

CCSS.HSF.TF.C.8
This video introduces the integration technique of trigonometric substitution, focusing on three types of integrals: those involving sqrt(a^2 - x^2), sqrt(a^2 + x^2), and sqrt(x^2 - a^2). The video explains how to use trigonometric identities to simplify these integrals by substituting x with trigonometric functions like sine, tangent, and secant. It also provides an example problem, demonstrating the process of substitution and the importance of sketching a right triangle to express the solution in terms of x. The video concludes with a caution about when to use trig substitution versus basic u substitution.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which identity is used to express cosine squared theta in terms of sine squared theta?

sec^2(theta) - 1 = tan^2(theta)

1 + tan^2(theta) = sec^2(theta)

sin^2(theta) + cos^2(theta) = 1

1 - sin^2(theta) = cos^2(theta)

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

For the integral involving the square root of a^2 - x^2, what substitution is used for x?

x = a sin(theta)

x = a tan(theta)

x = a cos(theta)

x = a sec(theta)

Tags

CCSS.HSF.TF.C.8

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What does the square root of a^2 - x^2 simplify to when x = a sin(theta)?

a cos(theta)

a sin(theta)

a sec(theta)

a tan(theta)

Tags

CCSS.HSF.TF.C.8

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

For the integral involving the square root of a^2 + x^2, what substitution is used for x?

x = a cos(theta)

x = a tan(theta)

x = a sin(theta)

x = a sec(theta)

Tags

CCSS.HSF.TF.C.8

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What does the square root of a^2 + x^2 simplify to when x = a tan(theta)?

a tan(theta)

a sec(theta)

a cos(theta)

a sin(theta)

Tags

CCSS.HSF.TF.C.8

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

For the integral involving the square root of x^2 - a^2, what substitution is used for x?

x = a cos(theta)

x = a tan(theta)

x = a sec(theta)

x = a sin(theta)

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What does the square root of x^2 - a^2 simplify to when x = a sec(theta)?

a sin(theta)

a cos(theta)

a sec(theta)

a tan(theta)

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