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sin2x/sinx
Solving integrals/ sin2x/sinx

Integral of sin2x/sinx dx

Limits of integration:

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The solution

You have entered [src] 
  1            
  /            
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 |  sin(2*x)   
 |  -------- dx
 |   sin(x)    
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0
∫01sin⁡(2x)sin⁡(x) dx\int\limits_{0}^{1} \frac{\sin{\left(2 x \right)}}{\sin{\left(x \right)}}\, dx 
Integral(sin(2*x)/sin(x), (x, 0, 1))
Detail solution

  1. There are multiple ways to do this integral.

    Method #1

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

      ∫2cos⁡(x) dx=2∫cos⁡(x) dx\int 2 \cos{\left(x \right)}\, dx = 2 \int \cos{\left(x \right)}\, dx

      1. The integral of cosine is sine:

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

      So, the result is: 2sin⁡(x)2 \sin{\left(x \right)}

    Method #2

    1. Rewrite the integrand:

      sin⁡(2x)sin⁡(x)=2cos⁡(x)\frac{\sin{\left(2 x \right)}}{\sin{\left(x \right)}} = 2 \cos{\left(x \right)}

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

      ∫2cos⁡(x) dx=2∫cos⁡(x) dx\int 2 \cos{\left(x \right)}\, dx = 2 \int \cos{\left(x \right)}\, dx

      1. The integral of cosine is sine:

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

      So, the result is: 2sin⁡(x)2 \sin{\left(x \right)}

  2. Add the constant of integration:

    2sin⁡(x)+constant2 \sin{\left(x \right)}+ \mathrm{constant}

The answer is:

2sin⁡(x)+constant2 \sin{\left(x \right)}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                          
 |                           
 | sin(2*x)                  
 | -------- dx = C + 2*sin(x)
 |  sin(x)                   
 |                           
/
∫sin⁡(2x)sin⁡(x) dx=C+2sin⁡(x)\int \frac{\sin{\left(2 x \right)}}{\sin{\left(x \right)}}\, dx = C + 2 \sin{\left(x \right)}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.9004
Plot the graph f(x)
The answer [src] 
2*sin(1)
2sin⁡(1)2 \sin{\left(1 \right)} 
=
= 
2*sin(1)
2sin⁡(1)2 \sin{\left(1 \right)}
Упростить
Numerical answer [src] 
1.68294196961579
1.68294196961579
The graph
Integral of sin2x/sinx dx

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

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