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(sinx+cosx)dx
Solving integrals/ (sinx+cosx)dx

Integral of (sinx+cosx)dx dx

Limits of integration:

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The graph:

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The solution

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 |  (sin(x) + cos(x)) dx
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∫01(sin⁡(x)+cos⁡(x)) dx\int\limits_{0}^{1} \left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)\, dx 
Integral(sin(x) + cos(x), (x, 0, 1))
Detail solution

  1. Integrate term-by-term:

    1. The integral of sine is negative cosine:

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

    1. The integral of cosine is sine:

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

    The result is: sin⁡(x)−cos⁡(x)\sin{\left(x \right)} - \cos{\left(x \right)}

  2. Now simplify:

    −2cos⁡(x+π4)- \sqrt{2} \cos{\left(x + \frac{\pi}{4} \right)}

  3. Add the constant of integration:

    −2cos⁡(x+π4)+constant- \sqrt{2} \cos{\left(x + \frac{\pi}{4} \right)}+ \mathrm{constant}

The answer is:

−2cos⁡(x+π4)+constant- \sqrt{2} \cos{\left(x + \frac{\pi}{4} \right)}+ \mathrm{constant}

The answer (Indefinite) [src] 
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 | (sin(x) + cos(x)) dx = C - cos(x) + sin(x)
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∫(sin⁡(x)+cos⁡(x)) dx=C+sin⁡(x)−cos⁡(x)\int \left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)\, dx = C + \sin{\left(x \right)} - \cos{\left(x \right)}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.902.5-2.5
Plot the graph f(x)
The answer [src] 
1 - cos(1) + sin(1)
−cos⁡(1)+sin⁡(1)+1- \cos{\left(1 \right)} + \sin{\left(1 \right)} + 1 
=
= 
1 - cos(1) + sin(1)
−cos⁡(1)+sin⁡(1)+1- \cos{\left(1 \right)} + \sin{\left(1 \right)} + 1 
1 - cos(1) + sin(1)
Numerical answer [src] 
1.30116867893976
1.30116867893976
The graph
Integral of (sinx+cosx)dx dx

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

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