Integration of Sin^2 x

Integration of Sin^2 x

Assessment

Interactive Video

Mathematics

9th - 12th Grade

Hard

Created by

Lucas Foster

FREE Resource

The video tutorial demonstrates the integration of sin^2 x. Initially, a u-substitution is considered but found unsuitable due to the absence of cosine x in the integrand. Instead, a power reducing formula is applied, transforming sin^2 x into a form involving cosine 2x. The integration is then split into two parts, requiring another u-substitution for cosine 2x. The final result is simplified using a double angle identity, offering an alternative expression for the antiderivative.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the initial substitution considered for integrating sin^2 x?

u = cos x

u = x^2

u = tan x

u = sin x

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Why does the initial u-substitution fail for integrating sin^2 x?

The integrand does not contain cos x

The integrand contains cos x

The integrand contains tan x

The integrand does not contain sin x

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What formula is used to rewrite sin^2 x for integration?

Double angle formula

Sum-to-product formula

Power-reducing formula

Product-to-sum formula

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the new substitution used to integrate cos 2x?

u = x

u = cos x

u = sin x

u = 2x

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the result of integrating 1 with respect to x?

1

x

0

2x

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the anti-derivative of sin u in terms of u?

sin u

cos u

-sin u

-cos u

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the constant of integration added to the anti-derivative?

D

E

C

F

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