How do I evaluate #intsin (pi x) cos (pi x) dx#?
I would use integration by parts where you have:
Where: Giving:
Hope it helps
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To evaluate the integral ∫sin(πx)cos(πx) dx, you can use the trigonometric identity sin(2θ) = 2sin(θ)cos(θ). By applying this identity, you can rewrite the integrand as 1/2 sin(2πx). Then, integrate 1/2 sin(2πx) with respect to x. The integral of sin(2πx) is -1/(2π)cos(2πx). So, the result of the integral is -1/(4π)cos(2πx) + 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.
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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