Mister Exam

Integral of 4cos2x-3sinx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
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 |  (4*cos(2*x) - 3*sin(x)) dx
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$$\int\limits_{0}^{1} \left(- 3 \sin{\left(x \right)} + 4 \cos{\left(2 x \right)}\right)\, dx$$
Integral(4*cos(2*x) - 3*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:

      1. The integral of sine is negative cosine:

      So, the result is:

    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:

    The result is:

  2. Now simplify:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                                      
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 | (4*cos(2*x) - 3*sin(x)) dx = C + 2*sin(2*x) + 3*cos(x)
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$$\int \left(- 3 \sin{\left(x \right)} + 4 \cos{\left(2 x \right)}\right)\, dx = C + 2 \sin{\left(2 x \right)} + 3 \cos{\left(x \right)}$$
The graph
The answer [src]
-3 + 2*sin(2) + 3*cos(1)
$$-3 + 3 \cos{\left(1 \right)} + 2 \sin{\left(2 \right)}$$
=
=
-3 + 2*sin(2) + 3*cos(1)
$$-3 + 3 \cos{\left(1 \right)} + 2 \sin{\left(2 \right)}$$
-3 + 2*sin(2) + 3*cos(1)
Numerical answer [src]
0.439501771255783
0.439501771255783

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