Mister Exam

Other calculators


dx/5+4sin(x)

Integral of dx/5+4sin(x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1                    
  /                    
 |                     
 |  (0.2 + 4*sin(x)) dx
 |                     
/                      
0                      
01(4sin(x)+0.2)dx\int\limits_{0}^{1} \left(4 \sin{\left(x \right)} + 0.2\right)\, dx
Integral(0.2 + 4*sin(x), (x, 0, 1))
Detail solution
  1. Integrate term-by-term:

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

      4sin(x)dx=4sin(x)dx\int 4 \sin{\left(x \right)}\, dx = 4 \int \sin{\left(x \right)}\, dx

      1. The integral of sine is negative cosine:

        sin(x)dx=cos(x)\int \sin{\left(x \right)}\, dx = - \cos{\left(x \right)}

      So, the result is: 4cos(x)- 4 \cos{\left(x \right)}

    1. The integral of a constant is the constant times the variable of integration:

      0.2dx=0.2x\int 0.2\, dx = 0.2 x

    The result is: 0.2x4cos(x)0.2 x - 4 \cos{\left(x \right)}

  2. Add the constant of integration:

    0.2x4cos(x)+constant0.2 x - 4 \cos{\left(x \right)}+ \mathrm{constant}


The answer is:

0.2x4cos(x)+constant0.2 x - 4 \cos{\left(x \right)}+ \mathrm{constant}

The answer (Indefinite) [src]
  /                                          
 |                                           
 | (0.2 + 4*sin(x)) dx = C - 4*cos(x) + 0.2*x
 |                                           
/                                            
(4sin(x)+0.2)dx=C+0.2x4cos(x)\int \left(4 \sin{\left(x \right)} + 0.2\right)\, dx = C + 0.2 x - 4 \cos{\left(x \right)}
The graph
0.001.000.100.200.300.400.500.600.700.800.90-1010
The answer [src]
4.2 - 4*cos(1)
4.24cos(1)4.2 - 4 \cos{\left(1 \right)}
=
=
4.2 - 4*cos(1)
4.24cos(1)4.2 - 4 \cos{\left(1 \right)}
4.2 - 4*cos(1)
Numerical answer [src]
2.03879077652744
2.03879077652744
The graph
Integral of dx/5+4sin(x) dx

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