# Integrate sin(x)dx: Typo in Calc Book

• Qube
Therefore, the correct answer is 2.In summary, the definite integral of sin(x) with b = ∏ and a = 0 is equal to 2. This can be found by using the fundamental theorem of calculus and the equation definite integral = F(b) - F(a). The anti-derivative of sin(x) is -cos(x), and plugging in b = ∏ and a = 0 gives F(∏) = -(-1) = 1 and F(0) = (-1), resulting in a final answer of 2. The book's answer of 2 is correct because the value of F(0) is -1, not 1.
Qube
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## Homework Statement

Integrate the definite integral ∫sin(x)dx given b = ∏ and a = 0.

## Homework Equations

Fundamental theorem of calculus; definite integral = F(b) - F(a)

## The Attempt at a Solution

The anti-derivative is -cos(x).

F(∏) = -(-1) = 1.
F(0) = 1.
F(b) - F(a) = 0.

Why does the book say the answer is 2 then?

Qube said:

## Homework Statement

Integrate the definite integral ∫sin(x)dx given b = ∏ and a = 0.

## Homework Equations

Fundamental theorem of calculus; definite integral = F(b) - F(a)

## The Attempt at a Solution

The anti-derivative is -cos(x).

F(∏) = -(-1) = 1.
F(0) = 1.
F(b) - F(a) = 0.

Why does the book say the answer is 2 then?

Because F(0)=(-1) not 1.

## 1. What is the correct way to integrate sin(x)dx?

The correct way to integrate sin(x)dx is to use the trigonometric identity ∫sin(x)dx = -cos(x) + C.

## 2. Is there a typo in the calculus book's instructions for integrating sin(x)dx?

Yes, it appears that there is a typo in the calculus book's instructions for integrating sin(x)dx. The correct identity should be ∫sin(x)dx = -cos(x) + C, not ∫sin(x)dx = cos(x) + C.

## 3. How can I check if my answer for integrating sin(x)dx is correct?

You can check if your answer for integrating sin(x)dx is correct by taking the derivative of your answer and seeing if it matches the original function, sin(x).

## 4. Can I use a different method to integrate sin(x)dx?

Yes, there are several methods you can use to integrate sin(x)dx, such as using substitution or integration by parts. However, the most efficient method for this particular integral is using the trigonometric identity.

## 5. What are the common mistakes to avoid when integrating sin(x)dx?

Some common mistakes to avoid when integrating sin(x)dx include forgetting the constant of integration, using the incorrect trigonometric identity, and making errors in algebraic simplification. It's important to carefully follow the steps and double check your work for accuracy.

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