Integral of sin x

How to solve the given integral by using the integral of sin x: formula, 1 example, and its solution.

Formula

Formula

The derivative of -cos x + C is
-[-sin x] = sin x.

Derivative of cos x

And integral and derivative
are the opposite operations.

The integral of sin x is
-cos x + C.

For an indefinite integral,
there should be +C.

Example

Example

Solution

(sin x/2 + cos x/2)2
= sin2 x/2 + 2(sin x/2)(cos x/2) + cos2 x/2

Square of a Sum

sin2 x/2 + cos2 x/2 = 1

Pythagorean Identity

2(sin x/2)(cos x/2) = sin 2⋅(x/2) = sin x

sin 2A

The integral of 1 is x.

Integral of a Polynomial

The integral of sin x is -cos x.

The given integral is an indefinite integral.
So write +C.

So x - cos x + C is the answer.