Integral of sinx formula

Formula

$\displaystyle \int{\sin{x} \,}dx \,=\, -\cos{x}+c$

Introduction

$x$ is a variable, which represents an angle of a right triangle, and the trigonometric sine function in terms of $x$ is written as $\sin{x}$ in mathematical form. The indefinite integral of $\sin{x}$ function with respect to $x$ is written in the following mathematical form in calculus.

$\displaystyle \int{\sin{x} \,}dx$

The integration of $\sin{x}$ function with respect to $x$ is equal to sum of the negative $\cos{x}$ and constant of integration.

$\displaystyle \int{\sin{x} \,}dx \,=\, -\cos{x}+c$

Alternative forms

The integration of sin function formula can be written in terms of any variable.

$(1) \,\,\,$ $\displaystyle \int{\sin{(b)} \,}db \,=\, -\cos{(b)}+c$

$(2) \,\,\,$ $\displaystyle \int{\sin{(h)} \,}dh \,=\, -\cos{(h)}+c$

$(3) \,\,\,$ $\displaystyle \int{\sin{(y)} \,}dy \,=\, -\cos{(y)}+c$

Proof

Learn how to derive the integration of sine function rule in integral calculus.