Mister Exam

Integral of cos(sqrt(x)) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1              
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 |     /  ___\   
 |  cos\\/ x / dx
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0                
$$\int\limits_{0}^{1} \cos{\left(\sqrt{x} \right)}\, dx$$
Integral(cos(sqrt(x)), (x, 0, 1))
Detail solution
  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. Use integration by parts:

        Let and let .

        Then .

        To find :

        1. The integral of cosine is sine:

        Now evaluate the sub-integral.

      2. The integral of sine is negative cosine:

      So, the result is:

    Now substitute back in:

  2. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                                     
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 | cos\\/ x / dx = C + 2*cos\\/ x / + 2*\/ x *sin\\/ x /
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$$\int \cos{\left(\sqrt{x} \right)}\, dx = C + 2 \sqrt{x} \sin{\left(\sqrt{x} \right)} + 2 \cos{\left(\sqrt{x} \right)}$$
The graph
The answer [src]
-2 + 2*cos(1) + 2*sin(1)
$$-2 + 2 \cos{\left(1 \right)} + 2 \sin{\left(1 \right)}$$
=
=
-2 + 2*cos(1) + 2*sin(1)
$$-2 + 2 \cos{\left(1 \right)} + 2 \sin{\left(1 \right)}$$
-2 + 2*cos(1) + 2*sin(1)
Numerical answer [src]
0.763546581352072
0.763546581352072
The graph
Integral of cos(sqrt(x)) dx

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