Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of 0dx
Integral of x^5/(x^2+1)
Integral of (x-2)^2dx
Integral of dr/r
Identical expressions
sin(sinx)cosx
sinus of ( sinus of x) co sinus of e of x
sinsinxcosx
sin(sinx)cosxdx

Solving integrals/ sin(sinx)cosx

Integral of sin(sinx)cosx dx

The solution

You have entered [src]

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

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

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

Detail solution

Let $u = \sin{\left(x \right)}$ .

Then let $du = \cos{\left(x \right)} dx$ and substitute $du$ :

$\int \sin{\left(u \right)}\, du$
1. The integral of sine is negative cosine:
  
  $\int \sin{\left(u \right)}\, du = - \cos{\left(u \right)}$
Now substitute $u$ back in:

$- \cos{\left(\sin{\left(x \right)} \right)}$
Add the constant of integration:

$- \cos{\left(\sin{\left(x \right)} \right)}+ \mathrm{constant}$

The answer is:

$- \cos{\left(\sin{\left(x \right)} \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

1 - cos(sin(1))

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

1 - cos(sin(1))

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

1 - cos(sin(1))

Numerical answer [src]

0.333633254607119

0.333633254607119

The graph

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

Other calculators

How to use it?

Identical expressions

Integral of sin(sinx)cosx dx

Limits of integration:

The graph:

Piecewise:

The solution