Math Doubts

Integral of cosx formula

Formula

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

Introduction

Take, $x$ is a variable and also represents an angle of a right triangle. Then, the trigonometric cosine function is mathematically written in terms of $x$ as $\cos{x}$. The indefinite integral of $\cos{x}$ function with respect to $x$ is expressed in mathematical form as follows.

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

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

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

Alternative forms

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

$(1) \,\,\,$ $\displaystyle \int{\cos{(g)} \,}dg \,=\, \sin{(g)}+c$

$(2) \,\,\,$ $\displaystyle \int{\cos{(m)} \,}dm \,=\, \sin{(m)}+c$

$(3) \,\,\,$ $\displaystyle \int{\cos{(z)} \,}dz \,=\, \sin{(z)}+c$

Proof

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

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