Mister Exam

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Integral of d{x}:
Integral of exp(x)*sin(x)
Integral of x^3*dx
Integral of exp(2*x)
Integral of sin(cosx)
Identical expressions
∫1_ three ^ four ▒〖√(𝑥−3)𝑑𝑥〗
∫1_3 to the power of 4▒〖√(𝑥−3)𝑑𝑥〗
∫1_ three to the power of four ▒〖√(𝑥−3)𝑑𝑥〗
∫1_34▒〖√(𝑥−3)𝑑𝑥〗
∫1_34▒〖√𝑥−3𝑑𝑥〗
∫1_3⁴▒〖√(𝑥−3)𝑑𝑥〗
∫1_3^4▒〖√𝑥−3𝑑𝑥〗

Integral of ∫1_3^4▒〖√(𝑥−3)𝑑𝑥〗 dx

The solution

You have entered [src]

  1                   
  /                   
 |                    
 |          _______   
 |  28561*\/ x - 3  dx
 |                    
/                     
0

$$\int\limits_{0}^{1} 28561 \sqrt{x - 3}\, dx$$

Integral(28561*sqrt(x - 3), (x, 0, 1))

Detail solution

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

$\int 28561 \sqrt{x - 3}\, dx = 28561 \int \sqrt{x - 3}\, dx$
1. Let $u = x - 3$ .
  
  Then let $du = dx$ and substitute $du$ :
  
  $\int \sqrt{u}\, du$
  1. The integral of $u^{n}$ is $\frac{u^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int \sqrt{u}\, du = \frac{2 u^{\frac{3}{2}}}{3}$
  Now substitute $u$ back in:
  
  $\frac{2 \left(x - 3\right)^{\frac{3}{2}}}{3}$
So, the result is: $\frac{57122 \left(x - 3\right)^{\frac{3}{2}}}{3}$
Now simplify:

$\frac{57122 \left(x - 3\right)^{\frac{3}{2}}}{3}$
Add the constant of integration:

$\frac{57122 \left(x - 3\right)^{\frac{3}{2}}}{3}+ \mathrm{constant}$

The answer is:

$\frac{57122 \left(x - 3\right)^{\frac{3}{2}}}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                         
 |                                       3/2
 |         _______          57122*(x - 3)   
 | 28561*\/ x - 3  dx = C + ----------------
 |                                 3        
/

$$\int 28561 \sqrt{x - 3}\, dx = C + \frac{57122 \left(x - 3\right)^{\frac{3}{2}}}{3}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

                           ___
          ___   114244*I*\/ 2 
57122*I*\/ 3  - --------------
                      3

$$- \frac{114244 \sqrt{2} i}{3} + 57122 \sqrt{3} i$$

                           ___
          ___   114244*I*\/ 2 
57122*I*\/ 3  - --------------
                      3

$$- \frac{114244 \sqrt{2} i}{3} + 57122 \sqrt{3} i$$

57122*i*sqrt(3) - 114244*i*sqrt(2)/3

Numerical answer [src]

(0.0 + 45083.0681566988j)

(0.0 + 45083.0681566988j)

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

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Identical expressions

Integral of ∫1_3^4▒〖√(𝑥−3)𝑑𝑥〗 dx

Limits of integration:

The graph:

Piecewise:

The solution