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

In summary, the conversation discusses the difficulty of marking up an image and the need to include the integral of -cos 6x in addition to ∫ 1 dx. It also suggests using double angle formulas to convert trig functions from 6x to 3x and confirms that multiplying - (1/12) in front of sin6x would be correct.
  • #1
Scholar1
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Member warned about posting without the template
IMG_8357.jpg


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

Thanks in advance!
 
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  • #2
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:
 
  • #3
So if I put - (1/12) in front of the sin6x it would be correct?
 
  • #4
Scholar1 said:
So if I put - (1/12) in front of the sin6x it would be correct?
Yesss...multiplication distributes over addition and subtraction.
 

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

What is an indefinite integral?

An indefinite integral is a mathematical concept used in calculus to find the most general antiderivative of a function. It is represented by the symbol ∫ f(x) dx, where f(x) is the function being integrated and dx represents the variable of integration. The result of an indefinite integral is a family of functions, rather than a single value.

How do you solve an indefinite integral problem?

To solve an indefinite integral problem, you need to use the rules of integration to find the antiderivative of the given function. These rules include the power rule, product rule, quotient rule, and chain rule. Once you have found the antiderivative, you can check your answer by taking the derivative of the result to see if it matches the original function.

What is the difference between an indefinite integral and a definite integral?

The main difference between an indefinite integral and a definite integral is that a definite integral has specific limits of integration, while an indefinite integral does not. A definite integral also gives a numerical value as the result, while an indefinite integral gives a family of functions as the result.

What are some real-world applications of indefinite integrals?

Indefinite integrals have many real-world applications, including calculating the total distance traveled by an object given its velocity function, finding the total cost of a variable rate of production, and determining the amount of radioactive material remaining after a certain amount of time.

Can you use technology to solve indefinite integral problems?

Yes, technology can be used to solve indefinite integral problems. Many graphing calculators and computer software programs have built-in integration functions that can quickly and accurately solve indefinite integrals. However, it is important to understand the concepts and rules of integration in order to use technology effectively and verify results.

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