Finding the Indefinite Integral: Can Multiplying a Constant Change the Solution?

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Homework Help Overview

The discussion revolves around finding the indefinite integral of a function, specifically examining how multiplying a constant affects the solution. The subject area is calculus, focusing on integration techniques and properties.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the implications of multiplying a constant with integrals, questioning how this affects the overall solution. There is an exploration of the correct application of integration rules and the use of trigonometric identities.

Discussion Status

The discussion is active, with participants sharing their attempts and seeking clarification on specific points. Some guidance has been offered regarding the distribution of multiplication over addition and subtraction in the context of integration.

Contextual Notes

There are indications of confusion regarding the proper setup of the integrals, particularly in relation to the constants and trigonometric functions involved. Participants express difficulty in marking up their attempts, which may affect clarity in communication.

Scholar1
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IMG_8357.jpg


I have posted my attempt and the problem above. Please help!

Thanks in advance!
 
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Scholar1 said:
IMG_8357.jpg


I have posted my attempt and the problem above. Please help!

Thanks in advance!
It's hard to mark up an image. :frown:

The factor of (1/2) multiplies not only ∫ 1 dx but also ∫ -cos 6x dx, which you omitted from the second integral. :frown:

After you have found the correct integrals, you can use the double angle formulas to convert these from trig functions in 6x to trig functions in 3x. :wink:
 
So if I put - (1/12) in front of the sin6x it would be correct?
 
Scholar1 said:
So if I put - (1/12) in front of the sin6x it would be correct?
Yesss...multiplication distributes over addition and subtraction.
 

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