Integral of x-3/4 dx

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$$\int\limits_{0}^{1} \left(x - \frac{3}{4}\right)\, dx$$

Integral(x - 3/4, (x, 0, 1))

Detail solution

Integrate term-by-term:
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x\, dx = \frac{x^{2}}{2}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int \left(- \frac{3}{4}\right)\, dx = - \frac{3 x}{4}$
The result is: $\frac{x^{2}}{2} - \frac{3 x}{4}$
Now simplify:

$\frac{x \left(2 x - 3\right)}{4}$
Add the constant of integration:

$\frac{x \left(2 x - 3\right)}{4}+ \mathrm{constant}$

The answer is:

$\frac{x \left(2 x - 3\right)}{4}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                    2      
 |                    x    3*x
 | (x - 3/4) dx = C + -- - ---
 |                    2     4 
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$$\int \left(x - \frac{3}{4}\right)\, dx = C + \frac{x^{2}}{2} - \frac{3 x}{4}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-1/4

$$- \frac{1}{4}$$

-1/4

$$- \frac{1}{4}$$

-1/4

Numerical answer [src]

-0.25

-0.25

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