How do you find the volume of the solid enclosed by the surface z=xsec^2(y) and the planes z=0, x=0,x=2,y=0, and y=π/4?

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Answer 1 · 2018-06-22T19:10:30

#= 2#

#int_V dV = int_(0)^(pi/4) dy int_(0)^(2) dx int_(0)^(x sec^2 y) dz#

#= int_(0)^(pi/4) dy int_(0)^(2) dx qquad x sec^2 y #

#= int_(0)^(pi/4) dy qquad [ x^2/2 sec^2 y ]_(0)^(2)#

#= int_(0)^(pi/4) dy qquad 2 sec^2 y #

#= [2 tan y]_(0)^(pi/4) = 2#