Integral of cos x
How to solve the given integral by using the integral of cos x: formula, 1 example, and its solution.
Formula
Recall that
the derivative of sin x is cos x.
And integral and derivative
are the opposite operations.
So the integral of cos x is
sin x + C.
For an indefinite integral,
there should be +C.
Example∫ cos2 x/2 dx
Solution
Solution (Detail)
cos2 x/2 = [1 + cos x]/2
cos A/2
Take the denomiator 1/2 out from the integral.
Solve the integral.
First write the coefficient 1/2.
The integral of 1 is x.
Integral of a Polynomial
The integral of cos x is sin x.
The given integral is an indefinite integral.
So write +C.
So
(1/2)(x + sin x) + C
is the answer.