Mister Exam

Integral of sinx+3cosx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1                       
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 |  (sin(x) + 3*cos(x)) dx
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$$\int\limits_{0}^{1} \left(\sin{\left(x \right)} + 3 \cos{\left(x \right)}\right)\, dx$$
Integral(sin(x) + 3*cos(x), (x, 0, 1))
Detail solution
  1. Integrate term-by-term:

    1. The integral of sine is negative cosine:

    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:

    The result is:

  2. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                              
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 | (sin(x) + 3*cos(x)) dx = C - cos(x) + 3*sin(x)
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$$\int \left(\sin{\left(x \right)} + 3 \cos{\left(x \right)}\right)\, dx = C + 3 \sin{\left(x \right)} - \cos{\left(x \right)}$$
The graph
The answer [src]
1 - cos(1) + 3*sin(1)
$$- \cos{\left(1 \right)} + 1 + 3 \sin{\left(1 \right)}$$
=
=
1 - cos(1) + 3*sin(1)
$$- \cos{\left(1 \right)} + 1 + 3 \sin{\left(1 \right)}$$
1 - cos(1) + 3*sin(1)
Numerical answer [src]
2.98411064855555
2.98411064855555
The graph
Integral of sinx+3cosx dx

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