Question

Help me: ="\int\limits^\pi _0 sin({x}) \, dx" alt="\int\limits^\pi _0 sin({x}) \, dx" align="absmiddle" class="latex-formula">

Answer 1

Answer:

$\int^{\pi}_{0}sin(x)dx = 2$

Step-by-step explanation:

To solve for the value of $\int^{\pi}_{0}sin(x)dx$, we need to first find the antiderivative of $sin(x)$.

Since the derivative of $cos(x)$ is $-sin(x)$, therefore the derivative of $-cos(x)$ is $sin(x)$. With this:

$\int^{\pi}_{0}sin(x)dx = -cos(\pi)-(-cos(0))$

$=-cos(\pi)+cos(0)$

$=-(-1)+1$

$=2$

∴ $\int^{\pi}_{0}sin(x)dx = 2$

Hope this helps :)