The definiteintegral2e⁽¹/ˣ³⁾ x⁴ dx, we first need to find the antiderivative of the integrand. We can do this by using substitution. Let u = 1/x³,then du/dx = -3/x⁴ , or dx = -du/(3x⁴ .) Substituting this expression for dx and simplifying, we get:∫ 2e⁽¹/ˣ³⁾ x⁴  dx = ∫ -2e^u du = -2e^u + CSubstituting back in for u, we get:-2e⁽¹/ˣ³⁾ + CTo evaluate the definite integral, we need to plug in the limits of integration, which are not given in the question. Without knowing the limits of integration, we cannot provide a specificnumericalanswer.The definite integral is represented as ∫[a, b] f(x) dx, where a and b are the lower and upper limits of integration, respectively. Can you please provide the limits ofintegrationfor the given function: 2 * 2e⁽¹/ˣ³⁾ * x⁴ dx.To know more aboutprobabilityvisit:-brainly.com/question/13604758#SPJ11...

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