How do you find the volume of the wedge-shaped region on the figure contained in the cylinder #x^2 + y^2 = 16# and bounded above by the plane #z = x# and below by the xy-plane? Calculus Using Integrals to Find Areas and Volumes Calculating Volume using Integrals 1 Answer A. S. Adikesavan Jul 19, 2018 # 128/3# cu Explanation: #V = int int z dx dy, x >= 0, z in [ 0, x ], and x^2 + y^2 <= 16# #= int x^2/2 dy, x^2 + y^2 <= 16.# #= 1/2 int (16- y^2 ) dy. y in [ -4, 4 ]# #=1/2 [ 16 y - y^3/3 ]#, between y = -4 and y = 4 # = 128/3# cu. Answer link Related questions How do you find the volume of a pyramid using integrals? How do you find the volume of the solid with base region bounded by the curve #9x^2+4y^2=36# if... How do you find the volume of the solid with base region bounded by the triangle with vertices... How do you find the volume of the solid with base region bounded by the curve #y=1-x^2# and the... How do you find the volume of the solid with base region bounded by the curve #y=1-x^2# and the... How do you use an integral to find the volume of a solid torus? How do you find the volume of the solid with base region bounded by the curves #y=1-x^2# and... How do you find the volume of the solid with base region bounded by the curve #y=e^x#, #y=ln4#,... How do you find the volume of a rotated region bounded by #y=sqrt(x)#, #y=3#, the y-axis about... How do you find the volume of the parallelepiped determined by the vectors: <1,3,7>, <2,1,5> and... See all questions in Calculating Volume using Integrals Impact of this question 17043 views around the world You can reuse this answer Creative Commons License