Mister Exam

Other calculators

cos(4x-3)dx
Solving integrals/ cos(4x-3)dx

Integral of cos(4x-3)dx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                
  /                
 |                 
 |  cos(4*x - 3) dx
 |                 
/                  
0
∫01cos⁡(4x−3) dx\int\limits_{0}^{1} \cos{\left(4 x - 3 \right)}\, dx 
Integral(cos(4*x - 3), (x, 0, 1))
Detail solution

  1. Let u=4x−3u = 4 x - 3.

    Then let du=4dxdu = 4 dx and substitute du4\frac{du}{4}:

    ∫cos⁡(u)4 du\int \frac{\cos{\left(u \right)}}{4}\, du

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

      ∫cos⁡(u) du=∫cos⁡(u) du4\int \cos{\left(u \right)}\, du = \frac{\int \cos{\left(u \right)}\, du}{4}

      1. The integral of cosine is sine:

        ∫cos⁡(u) du=sin⁡(u)\int \cos{\left(u \right)}\, du = \sin{\left(u \right)}

      So, the result is: sin⁡(u)4\frac{\sin{\left(u \right)}}{4}

    Now substitute uu back in:

    sin⁡(4x−3)4\frac{\sin{\left(4 x - 3 \right)}}{4}

  2. Now simplify:

    sin⁡(4x−3)4\frac{\sin{\left(4 x - 3 \right)}}{4}

  3. Add the constant of integration:

    sin⁡(4x−3)4+constant\frac{\sin{\left(4 x - 3 \right)}}{4}+ \mathrm{constant}

The answer is:

sin⁡(4x−3)4+constant\frac{\sin{\left(4 x - 3 \right)}}{4}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                  
 |                       sin(4*x - 3)
 | cos(4*x - 3) dx = C + ------------
 |                            4      
/
∫cos⁡(4x−3) dx=C+sin⁡(4x−3)4\int \cos{\left(4 x - 3 \right)}\, dx = C + \frac{\sin{\left(4 x - 3 \right)}}{4}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.902-2
Plot the graph f(x)
The answer [src] 
sin(1)   sin(3)
------ + ------
  4        4
sin⁡(3)4+sin⁡(1)4\frac{\sin{\left(3 \right)}}{4} + \frac{\sin{\left(1 \right)}}{4} 
=
= 
sin(1)   sin(3)
------ + ------
  4        4
sin⁡(3)4+sin⁡(1)4\frac{\sin{\left(3 \right)}}{4} + \frac{\sin{\left(1 \right)}}{4} 
sin(1)/4 + sin(3)/4
Numerical answer [src] 
0.245647748216941
0.245647748216941
The graph
Integral of cos(4x-3)dx dx

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

    © Mister Exam – Calculator