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Integral of -sinx dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
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0
∫01(−sin⁡(x)) dx\int\limits_{0}^{1} \left(- \sin{\left(x \right)}\right)\, dx 
Integral(-sin(x), (x, 0, 1))
Detail solution

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

    ∫(−sin⁡(x)) dx=−∫sin⁡(x) dx\int \left(- \sin{\left(x \right)}\right)\, dx = - \int \sin{\left(x \right)}\, dx

    1. The integral of sine is negative cosine:

      ∫sin⁡(x) dx=−cos⁡(x)\int \sin{\left(x \right)}\, dx = - \cos{\left(x \right)}

    So, the result is: cos⁡(x)\cos{\left(x \right)}

  2. Add the constant of integration:

    cos⁡(x)+constant\cos{\left(x \right)}+ \mathrm{constant}

The answer is:

cos⁡(x)+constant\cos{\left(x \right)}+ \mathrm{constant}

The answer (Indefinite) [src] 
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 | -sin(x) dx = C + cos(x)
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∫(−sin⁡(x)) dx=C+cos⁡(x)\int \left(- \sin{\left(x \right)}\right)\, dx = C + \cos{\left(x \right)}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.902-2
Plot the graph f(x)
The answer [src] 
-1 + cos(1)
−1+cos⁡(1)-1 + \cos{\left(1 \right)} 
=
= 
-1 + cos(1)
−1+cos⁡(1)-1 + \cos{\left(1 \right)} 
-1 + cos(1)
Numerical answer [src] 
-0.45969769413186
-0.45969769413186
The graph
Integral of -sinx dx

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

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