# Answer A or D for Calc Integration Question

• UrbanXrisis
In summary, the conversation is about solving a question involving the equation \frac{\sin^2{x}}{2}=\frac{-\cos 2x}{4}. The participants are discussing different methods and solutions, with one person ultimately finding the correct answer to be "D." They also mention the importance of considering antiderivatives in solving the problem.
UrbanXrisis

I got the answer down to letter A and D. Now I feel like it's letter A but not sure...

Last edited by a moderator:
Youre asking if $$\frac{sin^2(x)}{2} = \frac{-cos(2x)}{4}$$

Try x = 0

Or notice that f(x) = sin(x)cos(x) = sin(2x)/2, then the integral is real easy.

The easiest method is to differentiate each of the 3 results...

Daniel.

Take the derivative of each of the choices.

*Haha, too late

whozum said:
Youre asking if $$\frac{\sin^2{x}}{2}=\frac{-\cos 2x}{4}$$

Not at all. If F(x) is an antiderivative of f(x) then so is F(x)+C for any C. Here,

$$\frac{\sin^2 x}{2} = \left(-\frac{\cos 2x}{4}\right) + \frac{1}{4}$$

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dextercioby said:
The easiest method is to differentiate each of the 3 results...

Daniel.

how did you get III to be true?

look at my last post.

Convert f(x) to what I recommended and the integral evaluates to D directly.

Data said:
Not at all. If F(x) is an antiderivative of f(x) then so is F(x)+C for any C. Here,

$$\frac{\sin^2 x}{2} = \left(-\frac{\cos 2x}{4}\right) + \frac{1}{4}$$

Good call, I didnt see that.

## 1. How do I know whether to choose "A" or "D" for my calc integration question?

The decision between choosing "A" or "D" for a calc integration question ultimately depends on the specific problem you are solving. In general, "A" represents the area under the curve and "D" represents the derivative of the function. It is important to carefully read the problem and determine which of these is the most appropriate choice.

## 2. Can I use both "A" and "D" in the same problem?

Yes, it is possible to use both "A" and "D" in the same problem. This is known as the fundamental theorem of calculus, which states that the integral of a function is equal to the difference of its antiderivative evaluated at the upper and lower limits of integration.

## 3. What is the process for solving a problem using "A" or "D" for calc integration?

The process for solving a calc integration problem using "A" or "D" involves identifying the function to be integrated, determining the appropriate limits of integration, and then substituting the function and limits into the corresponding formula for "A" or "D". It is important to carefully follow each step and perform any necessary algebraic manipulations to simplify the problem.

## 4. Are there any common mistakes to avoid when using "A" or "D" for calc integration?

One common mistake to avoid when using "A" or "D" for calc integration is mixing up the upper and lower limits of integration. It is important to carefully read the problem and correctly identify which limit is which. Another mistake to avoid is forgetting to add the constant of integration when using "D", as the derivative of a function always has a constant term.

## 5. How can I check my answer when using "A" or "D" for calc integration?

You can check your answer when using "A" or "D" for calc integration by taking the derivative of your calculated antiderivative and comparing it to the original function. If they are equivalent, then your answer is likely correct. Additionally, you can use a graphing calculator or online tool to graph both the original function and the calculated antiderivative to visually confirm that they are the same.

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