Question

What isthe area bounded by and from `x=pi/4` to `x=(5pi)/4`?

A)Find the area bounded by and from `x=pi/4` to `x=(5pi)/4` Make an
accurate sketch of the graphs on the axes.

Answer 1

`A=A_(purp)+A_(red)=1-0.293=0.707`

Explanation:

If your question was find the area bounded by and from `x=pi/4` to `x=(5pi)/4` .

i think here you must suppose the function
like bounded by `y=sinx`

show below the wanted area (shaded) in the graph.

now let calculate the area:

`A=A_(purp)+A_(red)`

`color(purple)[A_(purp)=int_(pi/4)^pisinx*dx=[-cosx]_(pi/4)^pi]`

`color(purple)[=-cospi+cos(pi/4)=1+0=1]`

`color(red)[A_(red)=int_pi^(5pi/4)-sinx*dx=[cosx]_pi^(5pi/4)]`

`color(red)[=cospi-cos(5pi/4)=-1+1/sqrt2=0.707-1=-0.293]`

`A=A_(purp)+A_(red)=1-0.293=0.707`