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Identical expressions
sqrt(eight -x^ two)-2x
square root of (8 minus x squared ) minus 2x
square root of (eight minus x to the power of two) minus 2x
√(8-x^2)-2x
sqrt(8-x2)-2x
sqrt8-x2-2x
sqrt(8-x²)-2x
sqrt(8-x to the power of 2)-2x
sqrt8-x^2-2x
sqrt(8-x^2)-2xdx
Similar expressions
sqrt(8-x^2)+2x
sqrt(8+x^2)-2x

Solving integrals/ sqrt(8-x^2)-2x

Integral of sqrt(8-x^2)-2x dx

The solution

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  2                       
  /                       
 |                        
 |  /   ________      \   
 |  |  /      2       |   
 |  \\/  8 - x   - 2*x/ dx
 |                        
/                         
0

$$\int\limits_{0}^{2} \left(- 2 x + \sqrt{8 - x^{2}}\right)\, dx$$

Integral(sqrt(8 - x^2) - 2*x, (x, 0, 2))

Detail solution

Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- 2 x\right)\, dx = - \int 2 x\, dx$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int 2 x\, dx = 2 \int x\, dx$
    1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
      
      $\int x\, dx = \frac{x^{2}}{2}$
    So, the result is: $x^{2}$
  So, the result is: $- x^{2}$
The result is: $- x^{2} + \frac{x \sqrt{8 - x^{2}}}{2} + 4 \operatorname{asin}{\left(\frac{\sqrt{2} x}{4} \right)}$
Add the constant of integration:

$- x^{2} + \frac{x \sqrt{8 - x^{2}}}{2} + 4 \operatorname{asin}{\left(\frac{\sqrt{2} x}{4} \right)}+ \mathrm{constant}$

The answer is:

$- x^{2} + \frac{x \sqrt{8 - x^{2}}}{2} + 4 \operatorname{asin}{\left(\frac{\sqrt{2} x}{4} \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                                                 
 |                                                          ________
 | /   ________      \                     /    ___\       /      2 
 | |  /      2       |           2         |x*\/ 2 |   x*\/  8 - x  
 | \\/  8 - x   - 2*x/ dx = C - x  + 4*asin|-------| + -------------
 |                                         \   4   /         2      
/

$$\int \left(- 2 x + \sqrt{8 - x^{2}}\right)\, dx = C - x^{2} + \frac{x \sqrt{8 - x^{2}}}{2} + 4 \operatorname{asin}{\left(\frac{\sqrt{2} x}{4} \right)}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-2 + pi

$$-2 + \pi$$

-2 + pi

$$-2 + \pi$$

Упростить

Numerical answer [src]

1.14159265358979

1.14159265358979

The graph

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

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Integral of sqrt(8-x^2)-2x dx

Limits of integration:

The graph:

Piecewise:

The solution