Question

Find the area under the graph of f(x) = (1 + sin(x)) between the lines x = 0 and x = pi

Answer 1

Given:

$f(x)=1+sin(x)$

We will find the area under the graph of the function f(x)

To find the area, we will make the integration of the function from x = 0 and x =π

The area under the curve will be as follows:

$\begin{gathered} Area=\int_0^{\pi}f(x)dx=\int_0^{\pi}(1+sin(x))dx=(x-cos(x)) \\ \\ =(\pi-cos(\pi))-(0-cos(0))=(\pi-(-1))-(0-1)=5.1416 \end{gathered}$

So, the answer will be: Area = 5.1416