Mister Exam

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Integral of d{x}:
Integral of log(x)^2/x
Integral of e^u
Integral of x^3*e^x
Integral of sin^-1(x)
Identical expressions
(sinx/ two)^ two *cosx/ two
( sinus of x divide by 2) squared multiply by co sinus of e of x divide by 2
( sinus of x divide by two) to the power of two multiply by co sinus of e of x divide by two
(sinx/2)2*cosx/2
sinx/22*cosx/2
(sinx/2)²*cosx/2
(sinx/2) to the power of 2*cosx/2
(sinx/2)^2cosx/2
(sinx/2)2cosx/2
sinx/22cosx/2
sinx/2^2cosx/2
(sinx divide by 2)^2*cosx divide by 2
(sinx/2)^2*cosx/2dx

Solving integrals/ (sinx/2)^2*cosx/2

Integral of (sinx/2)^2*cosx/2 dx

The solution

You have entered [src]

  1                    
  /                    
 |                     
 |          2          
 |  /sin(x)\           
 |  |------| *cos(x)   
 |  \  2   /           
 |  ---------------- dx
 |         2           
 |                     
/                      
0

$$\int\limits_{0}^{1} \frac{\left(\frac{\sin{\left(x \right)}}{2}\right)^{2} \cos{\left(x \right)}}{2}\, dx$$

Integral((sin(x)/2)^2*cos(x)/2, (x, 0, 1))

Detail solution

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

$\int \frac{\left(\frac{\sin{\left(x \right)}}{2}\right)^{2} \cos{\left(x \right)}}{2}\, dx = \frac{\int \left(\frac{\sin{\left(x \right)}}{2}\right)^{2} \cos{\left(x \right)}\, dx}{2}$
1. Don't know the steps in finding this integral.
  
  But the integral is
  
  $\frac{\sin^{3}{\left(x \right)}}{12}$
So, the result is: $\frac{\sin^{3}{\left(x \right)}}{24}$
Add the constant of integration:

$\frac{\sin^{3}{\left(x \right)}}{24}+ \mathrm{constant}$

The answer is:

$\frac{\sin^{3}{\left(x \right)}}{24}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                 
 |                                  
 |         2                        
 | /sin(x)\                         
 | |------| *cos(x)             3   
 | \  2   /                  sin (x)
 | ---------------- dx = C + -------
 |        2                     24  
 |                                  
/

$${{\sin ^3x}\over{24}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

   3   
sin (1)
-------
   24

$${{\sin ^31}\over{24}}$$

   3   
sin (1)
-------
   24

$$\frac{\sin^{3}{\left(1 \right)}}{24}$$

Simplify

Numerical answer [src]

0.0248259681912898

0.0248259681912898

The graph

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

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Identical expressions

Integral of (sinx/2)^2*cosx/2 dx

Limits of integration:

The graph:

Piecewise:

The solution