Understanding the Integral of Cosine Squared

Understanding the Integral of Cosine Squared

Assessment

Interactive Video

Mathematics, Science

9th - 12th Grade

Practice Problem

Hard

Created by

Jackson Turner

FREE Resource

This video tutorial explains how to integrate the function cosine squared X DX. It begins with an introduction to the integration process and highlights the importance of using a power reducing formula for cosine squared. The tutorial then provides a detailed, step-by-step guide to integrating the function, including moving constants and handling derivatives. Finally, it presents the complete solution, emphasizing the inclusion of the constant of integration.

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6 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What formula is used to simplify the integral of cosine squared X?

Sum-to-product formula

Double angle formula

Power-reducing formula

Product-to-sum formula

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the integral of 1 with respect to X?

1

X^2

X

0

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

When integrating cosine, what function do we obtain?

Tangent

Cosine

Sine

Secant

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What must be done to the constant when integrating the expression?

Move it to the front

Ignore it

Divide it by 2

Multiply it by X

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the final expression for the integral of cosine squared X?

1/4 X + 1/2 sine 2X + C

1/2 X + 1/4 sine 2X + C

X + sine 2X + C

1/2 X + sine X + C

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Why is it important to include the constant C in the final expression?

It simplifies the expression

It is part of the power-reducing formula

It represents the derivative

It accounts for the constant of integration

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