# How do you integrate #int pisinpix dx#?

Using

Thus, we will let:

So, if we plug it back in:

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To integrate ( \int \sin(\pi x) , dx ), you can use the following steps:

- Identify the integral as a basic trigonometric integral.
- Apply the integration formula for the sine function: ( \int \sin(ax) , dx = -\frac{1}{a} \cos(ax) + C ), where ( a = \pi ).
- Substitute ( \pi x ) for ( ax ) in the formula.
- Integrate to get the result.

Applying these steps:

[ \int \sin(\pi x) , dx = -\frac{1}{\pi} \cos(\pi x) + C ]

Where ( C ) is the constant of integration.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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