Mister Exam

Integral of x^2cosx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1             
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 |   2          
 |  x *cos(x) dx
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0               
$$\int\limits_{0}^{1} x^{2} \cos{\left(x \right)}\, dx$$
Integral(x^2*cos(x), (x, 0, 1))
Detail solution
  1. Use integration by parts:

    Let and let .

    Then .

    To find :

    1. The integral of cosine is sine:

    Now evaluate the sub-integral.

  2. Use integration by parts:

    Let and let .

    Then .

    To find :

    1. The integral of sine is negative cosine:

    Now evaluate the sub-integral.

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

    1. The integral of cosine is sine:

    So, the result is:

  4. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                                    
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 |  2                             2                    
 | x *cos(x) dx = C - 2*sin(x) + x *sin(x) + 2*x*cos(x)
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$$\int x^{2} \cos{\left(x \right)}\, dx = C + x^{2} \sin{\left(x \right)} + 2 x \cos{\left(x \right)} - 2 \sin{\left(x \right)}$$
The graph
The answer [src]
-sin(1) + 2*cos(1)
$$- \sin{\left(1 \right)} + 2 \cos{\left(1 \right)}$$
=
=
-sin(1) + 2*cos(1)
$$- \sin{\left(1 \right)} + 2 \cos{\left(1 \right)}$$
-sin(1) + 2*cos(1)
Numerical answer [src]
0.239133626928383
0.239133626928383
The graph
Integral of x^2cosx dx

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