Determine the area between the curves y 8 7 sin and y 7

Determine the area between the curves y = 8 + 7 sin( ) and y = - 7 - 8 cos( ) on the interval - 9 x 3. Area between curve is

Solution

Area = intgral from -9 to 3 (8+7sin(pi*x/2)-(-7-8cospi*x/3)) = int(15+7sin(pi*x/2)+8cospi*x/3)) from -9 to 3 = 15*12 + int(7sin(pi*x/2)+8cospi*x/3)) from -9 to 3 = 180 + [-7*2/pi Cos(pi*x/2) +8*3/pi sin(pi*x/3)] from -9 to 3 = 180 + [-14/pi *sqrt(2) + 24/pi ] = 180 - 6.1 + 7.64 = 181.54