integral from 9/4 to 4 of sqrt(x)-(2x-6)

解答

\int_{\frac{9}{4}}^{4} x - (2 x - 6) d x

\frac{127}{48}

十进制

2.64583 \dots

求解步骤

\int_{\frac{9}{4}}^{4} x - (2 x - 6) d x

化简

= \int_{\frac{9}{4}}^{4} x - 2 x + 6 d x

使用积分加法定则:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{\frac{9}{4}}^{4} x d x - \int_{\frac{9}{4}}^{4} 2 x d x + \int_{\frac{9}{4}}^{4} 6 d x

\int_{\frac{9}{4}}^{4} x d x = \frac{37}{12}

\int_{\frac{9}{4}}^{4} 2 x d x = \frac{175}{16}

\int_{\frac{9}{4}}^{4} 6 d x = \frac{21}{2}

= \frac{37}{12} - \frac{175}{16} + \frac{21}{2}

化简

\frac{37}{12} - \frac{175}{16} + \frac{21}{2} : \frac{127}{48}

= \frac{127}{48}

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