Integral of sin(x)*cos(2)

The calculator will find the integral/antiderivative of $$$\sin{\left(x \right)} \cos{\left(2 \right)}$$$, with steps shown.

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Find $$$\int \sin{\left(x \right)} \cos{\left(2 \right)}\, dx$$$.

The trigonometric functions expect the argument in radians. To enter the argument in degrees, multiply it by pi/180, e.g. write 45° as 45*pi/180, or use the appropriate function adding 'd', e.g. write sin(45°) as sind(45).

Solution

Apply the constant multiple rule $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ with $$$c=\cos{\left(2 \right)}$$$ and $$$f{\left(x \right)} = \sin{\left(x \right)}$$$:

$${\color{red}{\int{\sin{\left(x \right)} \cos{\left(2 \right)} d x}}} = {\color{red}{\cos{\left(2 \right)} \int{\sin{\left(x \right)} d x}}}$$

The integral of the sine is $$$\int{\sin{\left(x \right)} d x} = - \cos{\left(x \right)}$$$:

$$\cos{\left(2 \right)} {\color{red}{\int{\sin{\left(x \right)} d x}}} = \cos{\left(2 \right)} {\color{red}{\left(- \cos{\left(x \right)}\right)}}$$

Therefore,

$$\int{\sin{\left(x \right)} \cos{\left(2 \right)} d x} = - \cos{\left(2 \right)} \cos{\left(x \right)}$$

Add the constant of integration:

$$\int{\sin{\left(x \right)} \cos{\left(2 \right)} d x} = - \cos{\left(2 \right)} \cos{\left(x \right)}+C$$

Answer

$$$\int \sin{\left(x \right)} \cos{\left(2 \right)}\, dx = - \cos{\left(2 \right)} \cos{\left(x \right)} + C$$$A

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Integral of $$$\sin{\left(x \right)} \cos{\left(2 \right)}$$$

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