Integral of sina×cosb dx

The solution

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 2*pi                
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  |  sin(a)*cos(b) db
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$$\int\limits_{0}^{2 \pi} \sin{\left(a \right)} \cos{\left(b \right)}\, db$$

Integral(sin(a)*cos(b), (b, 0, 2*pi))

Detail solution

The integral of a constant times a function is the constant times the integral of the function:

$\int \sin{\left(a \right)} \cos{\left(b \right)}\, db = \sin{\left(a \right)} \int \cos{\left(b \right)}\, db$
1. The integral of cosine is sine:
  
  $\int \cos{\left(b \right)}\, db = \sin{\left(b \right)}$
So, the result is: $\sin{\left(a \right)} \sin{\left(b \right)}$
Add the constant of integration:

$\sin{\left(a \right)} \sin{\left(b \right)}+ \mathrm{constant}$

The answer is:

$\sin{\left(a \right)} \sin{\left(b \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

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 | sin(a)*cos(b) db = C + sin(a)*sin(b)
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$$\int \sin{\left(a \right)} \cos{\left(b \right)}\, db = C + \sin{\left(a \right)} \sin{\left(b \right)}$$

Simplify

The answer [src]

$$0$$

Use the examples entering the upper and lower limits of integration.

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Identical expressions

Integral of sina×cosb dx

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The solution