Question

Integration of $2\sin x$?

Answer 1

Integration is a method of adding or summing up the parts to find the whole. It is a reverse process of differentiation, where we reduce the functions in smaller parts. Differentiation is the process of finding the derivative and integration is the process of finding the antiderivative of a function. So, these processes are inverse of each other. Here, we have to find the integration of the function $2\sin x$.

Complete step-by-step answer:
Here, we have to integrate the function $2\sin x$. So,
$\Rightarrow \int {2\sin x\,dx}$
Extracting $2$ from the integration as it is a constant. We get,
$\Rightarrow 2\int {\sin x\,dx}$
We know that the integration of the $\sin x$ is $- \cos x$.
Therefore,
$\Rightarrow 2\int {\sin x\,dx} = - 2\cos x + C$
Where $C$ is an integration constant.
Hence the integration of the function $2\sin x$ is $- 2\cos x + C$.

Note: The integration is the process of finding the antiderivative of a function. It is a similar way to add the slices to make it whole. The integration is the inverse process of differentiation. Integration is also called the anti-differentiation. The integration is used to find the volume, area and the central values of many things. Integration can be defined as $\int {F(x)dx = f(x) + C}$ where the function $F(x)$ is called anti=derivative or integral or primitive of the given function $f(x)$ and $C$ is known as the arbitrary constant or constant of integration.