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Integral of 3sin^2x*cosxdx dx

The solution

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 pi                    
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 2                     
  /                    
 |                     
 |       2             
 |  3*sin (x)*cos(x) dx
 |                     
/                      
0

$$\int\limits_{0}^{\frac{\pi}{2}} 3 \sin^{2}{\left(x \right)} \cos{\left(x \right)}\, dx$$

Integral((3*sin(x)^2)*cos(x), (x, 0, pi/2))

Detail solution

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

Then let $du = \cos{\left(x \right)} dx$ and substitute $3 du$ :

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

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

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

The answer is:

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

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

$$1$$

Numerical answer [src]

1.0

1.0

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

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Identical expressions

Integral of 3sin^2x*cosxdx dx

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The solution