Mister Exam

Other calculators

e^(x/3)
Solving integrals/ e^(x/3)

Integral of e^(x/3) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1      
  /      
 |       
 |   x   
 |   -   
 |   3   
 |  E  dx
 |       
/        
0
$$\int\limits_{0}^{1} e^{\frac{x}{3}}\, dx$$ 
Integral(E^(x/3), (x, 0, 1))
Detail solution

  1. Let .

    Then let and substitute :

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

      1. The integral of the exponential function is itself.

      So, the result is:

    Now substitute back in:

  2. Now simplify:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                
 |                 
 |  x             x
 |  -             -
 |  3             3
 | E  dx = C + 3*e 
 |                 
/
$$\int e^{\frac{x}{3}}\, dx = C + 3 e^{\frac{x}{3}}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
        1/3
-3 + 3*e
$$-3 + 3 e^{\frac{1}{3}}$$ 
=
= 
        1/3
-3 + 3*e
$$-3 + 3 e^{\frac{1}{3}}$$ 
-3 + 3*exp(1/3)
Numerical answer [src] 
1.18683727525827
1.18683727525827
The graph
Integral of e^(x/3) dx

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

    © Mister Exam – Calculator