integral from 1 to 8 of |t^2-4t-12|

解答

\int_{1}^{8} t^{2} - 4 t - 12 d t

77

求解步骤

\int_{1}^{8} t^{2} - 4 t - 12 d t

拿掉绝对值

= \int_{1}^{6} - t^{2} + 4 t + 12 d t + \int_{6}^{8} t^{2} - 4 t - 12 d t

\int_{1}^{6} - t^{2} + 4 t + 12 d t = \frac{175}{3}

\int_{6}^{8} t^{2} - 4 t - 12 d t = \frac{56}{3}

= \frac{175}{3} + \frac{56}{3}

化简

\frac{175}{3} + \frac{56}{3} : 77

= 77

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