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.
enter image source here

1 Answer
May 23, 2018

#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.

desmos.com

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#