Mister Exam

Other calculators

x^(33/10)/5
Solving integrals/ x^(33/10)/5

Integral of x^(33/10)/5 dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1       
  /       
 |        
 |   33   
 |   --   
 |   10   
 |  x     
 |  --- dx
 |   5    
 |        
/         
0
∫01x33105 dx\int\limits_{0}^{1} \frac{x^{\frac{33}{10}}}{5}\, dx 
Integral(x^(33/10)/5, (x, 0, 1))
Detail solution

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

    ∫x33105 dx=∫x3310 dx5\int \frac{x^{\frac{33}{10}}}{5}\, dx = \frac{\int x^{\frac{33}{10}}\, dx}{5}

    1. The integral of xnx^{n} is xn+1n+1\frac{x^{n + 1}}{n + 1} when n≠−1n \neq -1:

      ∫x3310 dx=10x431043\int x^{\frac{33}{10}}\, dx = \frac{10 x^{\frac{43}{10}}}{43}

    So, the result is: 2x431043\frac{2 x^{\frac{43}{10}}}{43}

  2. Add the constant of integration:

    2x431043+constant\frac{2 x^{\frac{43}{10}}}{43}+ \mathrm{constant}

The answer is:

2x431043+constant\frac{2 x^{\frac{43}{10}}}{43}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                  
 |                   
 |  33             43
 |  --             --
 |  10             10
 | x            2*x  
 | --- dx = C + -----
 |  5             43 
 |                   
/
∫x33105 dx=C+2x431043\int \frac{x^{\frac{33}{10}}}{5}\, dx = C + \frac{2 x^{\frac{43}{10}}}{43}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.900.00.4
Plot the graph f(x)
The answer [src] 
2/43
243\frac{2}{43} 
=
= 
2/43
243\frac{2}{43} 
2/43
Numerical answer [src] 
0.0465116279069767
0.0465116279069767
The graph
Integral of x^(33/10)/5 dx

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

    © Mister Exam – Calculator