Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of sec^3(x)
Integral of e^y
Integral of |x|
Integral of xe^(x^2)
Identical expressions
sqrt(thirty-six -9x^ two)- three
square root of (36 minus 9x squared ) minus 3
square root of (thirty minus six minus 9x to the power of two) minus three
√(36-9x^2)-3
sqrt(36-9x2)-3
sqrt36-9x2-3
sqrt(36-9x²)-3
sqrt(36-9x to the power of 2)-3
sqrt36-9x^2-3
sqrt(36-9x^2)-3dx
Similar expressions
sqrt(36+9x^2)-3
sqrt(36-9x^2)+3

Solving integrals/ sqrt(36-9x^2)-3

Integral of sqrt(36-9x^2)-3 dx

The solution

You have entered [src]

  2                        
  /                        
 |                         
 |  /   ___________    \   
 |  |  /         2     |   
 |  \\/  36 - 9*x   - 3/ dx
 |                         
/                          
-2

$$\int\limits_{-2}^{2} \left(\sqrt{- 9 x^{2} + 36} - 3\right)\, dx$$

Integral(sqrt(36 - 9*x^2) - 1*3, (x, -2, 2))

Detail solution

Integrate term-by-term:
1. The integral of a constant is the constant times the variable of integration:
  
  $\int \left(\left(-1\right) 3\right)\, dx = - 3 x$
The result is: $\frac{x \sqrt{36 - 9 x^{2}}}{2} - 3 x + 6 \operatorname{asin}{\left(\frac{x}{2} \right)}$
Now simplify:

$\frac{3 x \sqrt{4 - x^{2}}}{2} - 3 x + 6 \operatorname{asin}{\left(\frac{x}{2} \right)}$
Add the constant of integration:

$\frac{3 x \sqrt{4 - x^{2}}}{2} - 3 x + 6 \operatorname{asin}{\left(\frac{x}{2} \right)}+ \mathrm{constant}$

The answer is:

$\frac{3 x \sqrt{4 - x^{2}}}{2} - 3 x + 6 \operatorname{asin}{\left(\frac{x}{2} \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                                                
 |                                                      ___________
 | /   ___________    \                                /         2 
 | |  /         2     |                      /x\   x*\/  36 - 9*x  
 | \\/  36 - 9*x   - 3/ dx = C - 3*x + 6*asin|-| + ----------------
 |                                           \2/          2        
/

$${{x\,\sqrt{36-9\,x^2}}\over{2}}-3\,x+6\,\arcsin \left({{x}\over{2}} \right)$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-12 + 6*pi

$$6\,\pi-12$$

-12 + 6*pi

$$-12 + 6 \pi$$

Simplify

Numerical answer [src]

6.84955592153876

6.84955592153876

The graph

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

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of sqrt(36-9x^2)-3 dx

Limits of integration:

The graph:

Piecewise:

The solution