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Solving integrals/ y=10^-x

Integral of y=10^-x dx

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$$\int\limits_{0}^{1} 10^{- x}\, dx$$

Integral(10^(-x), (x, 0, 1))

Detail solution

Let $u = - x$ .

Then let $du = - dx$ and substitute $- du$ :

$\int \left(- 10^{u}\right)\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 10^{u}\, du = - \int 10^{u}\, du$
  1. The integral of an exponential function is itself divided by the natural logarithm of the base.
    
    $\int 10^{u}\, du = \frac{10^{u}}{\log{\left(10 \right)}}$
  So, the result is: $- \frac{10^{u}}{\log{\left(10 \right)}}$
Now substitute $u$ back in:

$- \frac{10^{- x}}{\log{\left(10 \right)}}$
Add the constant of integration:

$- \frac{10^{- x}}{\log{\left(10 \right)}}+ \mathrm{constant}$

The answer is:

$- \frac{10^{- x}}{\log{\left(10 \right)}}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                     
 |                   -x 
 |   -x            10   
 | 10   dx = C - -------
 |               log(10)
/

$$\int 10^{- x}\, dx = C - \frac{10^{- x}}{\log{\left(10 \right)}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

    9     
----------
10*log(10)

$$\frac{9}{10 \log{\left(10 \right)}}$$

    9     
----------
10*log(10)

$$\frac{9}{10 \log{\left(10 \right)}}$$

9/(10*log(10))

Numerical answer [src]

0.390865033712927

0.390865033712927

The graph

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