$$\int_0^1 \int_0^z \int_y^z z\sin(x^2) \,\mathrm dx\,\mathrm dy\,\mathrm dz$$
I don't have any idea about how to graph given region. to me, intuitively this is not easy to imagine. somebody can analyze this integral?
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1So reading from the left we see z ranges from 0 to 1. Then the next interval says y takes all values from y=0 to y=z. This means the region is bounded by the line y=z in the yz-plane --- stopping at y=z=1. Finally the inner-most integral tells us the region is bounded further by the lines x=y in the xy-plane and x=z in the xz-plane. Once you draw these on a set of xyz-axes the region may become clear. It looks like an upside-down pyramid in the positive xyz-region. Vertices at (0,0,1) (0,1,1) (1,1,1) (1,0,1) and (0,0,0) – User0112358 Nov 03 '15 at 11:12
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Amazing!! I understood. Really thanks for your comment – fbg Nov 03 '15 at 11:24