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The given integral is, ∫x210x3dx Using substitution method of integration, on substituting x3 with t x3=t 3x2dx=dt x2dx=dt3 Then the transformed integral we get is, I=∫10t3dt =13∫10tdt Using exponential rule, ∫axdx=axln(a)+C I=13∫10tdt =13[10tln(10)]+C On puttinf back the value of t, we get I=10x33ln(10)+C Therefore, the value of the given integral is 10x33ln(10)+C
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Find the area of the part of the plane 5x+4y+z=20 that lies in the first octant.
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