To integrate the expression 1 sin(x), we can rewrite it as sin(x).
The integral of sin(x) is a common integral that most calculus students learn. The result is:
∫ sin(x) dx = -cos(x) + C
Where C represents the constant of integration. The reason behind this integration is based on the fundamental theorem of calculus, which relates differentiation and integration.
To understand why the integral of sin(x) results in -cos(x), remember that the derivative of -cos(x) is sin(x).
Thus, if you are ever unsure, you can always differentiate your result to check:
d/dx (-cos(x)) = sin(x)
This confirms that our integration is correct. In summary, the integral of 1 sin(x) or simply sin(x) is:
∫ sin(x) dx = -cos(x) + C