Integral of sin(x)+cos(x) dx

The solution

You have entered [src]

  1                     
  /                     
 |                      
 |  (sin(x) + cos(x)) dx
 |                      
/                       
0

$$\int\limits_{0}^{1} \left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)\, dx$$

Integral(sin(x) + cos(x), (x, 0, 1))

Detail solution

Integrate term-by-term:
1. The integral of sine is negative cosine:
  
  $\int \sin{\left(x \right)}\, dx = - \cos{\left(x \right)}$
1. The integral of cosine is sine:
  
  $\int \cos{\left(x \right)}\, dx = \sin{\left(x \right)}$
The result is: $\sin{\left(x \right)} - \cos{\left(x \right)}$
Now simplify:

$- \sqrt{2} \cos{\left(x + \frac{\pi}{4} \right)}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

  /                                          
 |                                           
 | (sin(x) + cos(x)) dx = C - cos(x) + sin(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

Plot the graph f(x)

The answer [src]

1 - cos(1) + sin(1)

$$- \cos{\left(1 \right)} + \sin{\left(1 \right)} + 1$$

1 - cos(1) + sin(1)

$$- \cos{\left(1 \right)} + \sin{\left(1 \right)} + 1$$

1 - cos(1) + sin(1)

Numerical answer [src]

1.30116867893976

1.30116867893976

The graph

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

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of sin(x)+cos(x) dx

Limits of integration:

The graph:

Piecewise:

The solution