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cos^(2)7x

Integral of cos^(2)7x dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src]
  1             
  /             
 |              
 |     2        
 |  cos (7*x) dx
 |              
/               
0               
$$\int\limits_{0}^{1} \cos^{2}{\left(7 x \right)}\, dx$$
Integral(cos(7*x)^2, (x, 0, 1))
Detail solution
  1. Rewrite the integrand:

  2. Integrate term-by-term:

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

      1. Let .

        Then let and substitute :

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

          1. The integral of cosine is sine:

          So, the result is:

        Now substitute back in:

      So, the result is:

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

    The result is:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                
 |                                 
 |    2               x   sin(14*x)
 | cos (7*x) dx = C + - + ---------
 |                    2       28   
/                                  
$${{{{\sin \left(14\,x\right)}\over{2}}+7\,x}\over{14}}$$
The graph
The answer [src]
1   cos(7)*sin(7)
- + -------------
2         14     
$${{\sin 14+14}\over{28}}$$
=
=
1   cos(7)*sin(7)
- + -------------
2         14     
$$\frac{\sin{\left(7 \right)} \cos{\left(7 \right)}}{14} + \frac{1}{2}$$
Numerical answer [src]
0.53537883413196
0.53537883413196
The graph
Integral of cos^(2)7x dx

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