Calculus Help NET AREA

Question

Find the net area and the are of the region bounded by y=10cos(x) and the x-axis between x= -π/2 and x=π.

 

Answer 1

The cosine function will be zero at -π/2 and π/2.  From 0 to π, equal parts will be above and below the x-axis, so the area in this interval will be zero.

 

∫10cos(x) dx =  10 sin(x) from -π/2 to 0 =

 

10 sin(0) - 10 sin(-π/2) = 10

 

 

The net area is 10 square units.

 

 

 

The area should be the same when we integrate from -π/2 to π:

 

∫10 cos(x) dx = 10 sin(x) from -π/2 to π =

 

10 sin(π) - 10 sin(-π/2) = 10