How do you find the area of the region bounded by the curves #y=sin(x)#, #y=e^x#, #x=0#, and #x=pi/2# ? Calculus Using Integrals to Find Areas and Volumes Calculating Areas using Integrals 1 Answer AJ Speller Sep 22, 2014 Over the interval #[0,pi/2]# the function #y=e^x# is greater that the function #y=sin(x)#. This is why #y=sin(x)# is subtracted from #y=e^x#. #int_0^(pi/2)e^x-sin(x)dx# #=[e^x-(-cos(x))]_0^(pi/2)# #=[e^x+cos(x)]_0^(pi/2)# #=[e^(pi/2)+cos(pi/2)-(e^0+cos(0))]# #=[e^(pi/2)+0-(1+1)]# #=[e^(pi/2)-(2)]# #=[e^(pi/2)-2]# #=2.81048-># Solution Answer link Related questions How do you find the area of circle using integrals in calculus? How do you find the area between two curves using integrals? How do you find the area of an ellipse using integrals? How do you find the area under a curve using integrals? How do you find the area of the region between the curves #y=x-1# and #y^2=2x+6# ? How do you find the area of the region bounded by the curves #y=1+sqrt(x)# and #y=1+x/3# ? How do you find the area of the region bounded by the curves #y=|x|# and #y=x^2-2# ? How do you find the area of the region bounded by the curves #y=tan(x)# and #y=2sin(x)# on the... How do I find the area between the curves #y=x^2-4x+3# and #y=3+4x-x^2#? How do you find the area between the curves #x+3y=21# and #x+7=y^2#? See all questions in Calculating Areas using Integrals Impact of this question 20234 views around the world You can reuse this answer Creative Commons License