Evaluate
\frac{3\pi ^{2}X}{8}
Differentiate w.r.t. X
\frac{3 \pi ^ {2}}{8} = 3.7011016504085092
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\int xX\mathrm{d}x
Evaluate the indefinite integral first.
X\int x\mathrm{d}x
Factor out the constant using \int af\left(x\right)\mathrm{d}x=a\int f\left(x\right)\mathrm{d}x.
X\times \frac{x^{2}}{2}
Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int x\mathrm{d}x with \frac{x^{2}}{2}.
\frac{Xx^{2}}{2}
Simplify.
\frac{1}{2}X\pi ^{2}-\frac{1}{2}X\times \left(\frac{1}{2}\pi \right)^{2}
The definite integral is the antiderivative of the expression evaluated at the upper limit of integration minus the antiderivative evaluated at the lower limit of integration.
\frac{3X\pi ^{2}}{8}
Simplify.
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