V=∭dV=∫01∫x2x∫0x+y+15dzdydx=∫01∫x2xx+y+15dydx=∫01[xy+1/2y2+15y]x2xdx=∫01xx+1/2x+15x−x3−1/2x4−15x2dx=2/5x5/2+1/4x2+10x3/2−1/4x4−1/10x5−5x3∣01=2/5+1/4+10−1/4−1/10−5=5.3V = \iiint dV = \int_0^1 \int_{x^2}^{\sqrt x} \int_0^{x+y+15}dzdydx \\ = \int_0^1 \int_{x^2}^{\sqrt x} x + y+15 dydx \\ = \int_0^1 \Big[xy + 1/2y^2 + 15y\Big]_{x^2}^{\sqrt x} dx \\ = \int_0^1 x\sqrt x + 1/2x+ 15\sqrt x - x^3 - 1/2x^4 - 15x^2 dx \\ = 2/5x^{5/2} + 1/4 x^2 + 10x^{3/2} - 1/4x^4 - 1/10x^5 - 5x^3\Big|_0^1 \\ = 2/5 + 1/4 + 10 - 1/4 - 1/10 - 5 = 5.3V=∭dV=∫01∫x2x∫0x+y+15dzdydx=∫01∫x2xx+y+15dydx=∫01[xy+1/2y2+15y]x2xdx=∫01xx+1/2x+15x−x3−1/2x4−15x2dx=2/5x5/2+1/4x2+10x3/2−1/4x4−1/10x5−5x3∣∣01=2/5+1/4+10−1/4−1/10−5=5.3
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