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Similar expressions
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Solving integrals/ (x^2-cosx)dx

Integral of (x^2-cosx)dx dx

The solution

You have entered [src]

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

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

Integral(x^2 - cos(x), (x, 0, 1))

Detail solution

Integrate term-by-term:
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x^{2}\, dx = \frac{x^{3}}{3}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- \cos{\left(x \right)}\right)\, dx = - \int \cos{\left(x \right)}\, dx$
  1. The integral of cosine is sine:
    
    $\int \cos{\left(x \right)}\, dx = \sin{\left(x \right)}$
  So, the result is: $- \sin{\left(x \right)}$
The result is: $\frac{x^{3}}{3} - \sin{\left(x \right)}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

1/3 - sin(1)

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

1/3 - sin(1)

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

1/3 - sin(1)

Numerical answer [src]

-0.508137651474563

-0.508137651474563

The graph

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

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Identical expressions

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Integral of (x^2-cosx)dx dx

Limits of integration:

The graph:

Piecewise:

The solution