Processing Math: Done

Aus Online Mathematik Brückenkurs 2

The integral is a standard integral, with 5x as the argument of the cosine function. If we therefore substitute u=5x, we obtain the “correct” argument of the cosine,

0cos5xdx=u=5xdu=5xdx=5dx=5150cosudu

As can be seen, the variable change replaced dx by 51du and the new limits of integration become u=50=0 and u=5=5.

Now, we have a standard integral which can easily compute:

5150cosudu=51sinu05=51sin5−sin0=510−0=0

NOTE: if we draw the graph for y=cos5x, we see also that the area between the curve and x -axis above the x -axis is the same as the area under the x -axis.