积分 cos(3)x dx

You have entered [src]

 pi            
  /            
 |             
 |  cos(3)*x dx
 |             
/              
0

$$\int\limits_{0}^{\pi} x \cos{\left(3 \right)}\, dx$$

Integral(cos(3)*x, (x, 0, pi))

Detail solution

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

$\int x \cos{\left(3 \right)}\, dx = \cos{\left(3 \right)} \int x\, dx$
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x\, dx = \frac{x^{2}}{2}$
So, the result is: $\frac{x^{2} \cos{\left(3 \right)}}{2}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

  /                   2       
 |                   x *cos(3)
 | cos(3)*x dx = C + ---------
 |                       2    
/

$$\int x \cos{\left(3 \right)}\, dx = C + \frac{x^{2} \cos{\left(3 \right)}}{2}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

  2       
pi *cos(3)
----------
    2

$$\frac{\pi^{2} \cos{\left(3 \right)}}{2}$$

  2       
pi *cos(3)
----------
    2

$$\frac{\pi^{2} \cos{\left(3 \right)}}{2}$$

pi^2*cos(3)/2

Numerical answer [src]

-4.8854171507466

-4.8854171507466

这些示例也可用于输入定积分的上下限.