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Differentiate w.r.t. B
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\int Bt^{2}\mathrm{d}x
Evaluate the indefinite integral first.
Bt^{2}x
Find the integral of Bt^{2} using the table of common integrals rule \int a\mathrm{d}x=ax.
Bt^{2}\times 4-Bt^{2}\times 0
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.
4Bt^{2}
Simplify.