By the Fundamental Theorem of Calculus, if we can find a function Z such that dZ/dX = Y, then

Z(R) - Z(-R) = _{-R}∫^{R}Y dx.^{ }_{ } |

Z = H*X - (H/R^{2})*X^{3}/3,^{ }_{ } |

dZ/dX = H - (H/R^{2})*X^{2}= Y,^{ }_{ } |

Z(R) - Z(-R) = 4/3*H*R = 2/3*B*H^{ }_{ } |

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