Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of x^(-2)
Integral of sin(3x)
Integral of logx
Integral of x^2/(1+x)
Identical expressions
(sin^2x*cosx)
( sinus of squared x multiply by co sinus of e of x)
(sin2x*cosx)
sin2x*cosx
(sin²x*cosx)
(sin to the power of 2x*cosx)
(sin^2xcosx)
(sin2xcosx)
sin2xcosx
sin^2xcosx
(sin^2x*cosx)dx

Integral of (sin^2x*cosx) dx

The solution

You have entered [src]

  2                  
  /                  
 |                   
 |     2             
 |  sin (x)*cos(x) dx
 |                   
/                    
0

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

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

Detail solution

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

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

$\int u^{2}\, du$
1. The integral of $u^{n}$ is $\frac{u^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int u^{2}\, du = \frac{u^{3}}{3}$
Now substitute $u$ back in:

$\frac{\sin^{3}{\left(x \right)}}{3}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

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

$$\int \sin^{2}{\left(x \right)} \cos{\left(x \right)}\, dx = C + \frac{\sin^{3}{\left(x \right)}}{3}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

   3   
sin (2)
-------
   3

$$\frac{\sin^{3}{\left(2 \right)}}{3}$$

   3   
sin (2)
-------
   3

$$\frac{\sin^{3}{\left(2 \right)}}{3}$$

sin(2)^3/3

Numerical answer [src]

0.250608981556331

0.250608981556331

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

Other calculators

How to use it?

Identical expressions

Integral of (sin^2x*cosx) dx

Limits of integration:

The graph:

Piecewise:

The solution