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Identical expressions
-sint*(cost)^ two
minus sinus of t multiply by ( co sinus of e of t) squared
minus sinus of t multiply by ( co sinus of e of t) to the power of two
-sint*(cost)2
-sint*cost2
-sint*(cost)²
-sint*(cost) to the power of 2
-sint(cost)^2
-sint(cost)2
-sintcost2
-sintcost^2
Similar expressions
sint*(cost)^2

Solving integrals/ -sint*(cost)^2

Integral of -sint*(cost)^2 dx

The solution

You have entered [src]

  1                   
  /                   
 |                    
 |             2      
 |  -sin(t)*cos (t) dt
 |                    
/                     
0

$$\int\limits_{0}^{1} - \sin{\left(t \right)} \cos^{2}{\left(t \right)}\, dt$$

Integral((-sin(t))*cos(t)^2, (t, 0, 1))

Detail solution

Let $u = \cos{\left(t \right)}$ .

Then let $du = - \sin{\left(t \right)} dt$ 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:

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

$\frac{\cos^{3}{\left(t \right)}}{3}+ \mathrm{constant}$

The answer is:

$\frac{\cos^{3}{\left(t \right)}}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                
 |                             3   
 |            2             cos (t)
 | -sin(t)*cos (t) dt = C + -------
 |                             3   
/

$$\int - \sin{\left(t \right)} \cos^{2}{\left(t \right)}\, dt = C + \frac{\cos^{3}{\left(t \right)}}{3}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

         3   
  1   cos (1)
- - + -------
  3      3

$$- \frac{1}{3} + \frac{\cos^{3}{\left(1 \right)}}{3}$$

         3   
  1   cos (1)
- - + -------
  3      3

$$- \frac{1}{3} + \frac{\cos^{3}{\left(1 \right)}}{3}$$

-1/3 + cos(1)^3/3

Numerical answer [src]

-0.280757131583002

-0.280757131583002

The graph

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

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Identical expressions

Similar expressions

Integral of -sint*(cost)^2 dx

Limits of integration:

The graph:

Piecewise:

The solution