integral from 1 to 2 of x^2+1/(x^4)

解答

\int_{1}^{2} x^{2} + \frac{1}{x ^{4}} d x

\frac{21}{8}

十进制

2.625

求解步骤

\int_{1}^{2} x^{2} + \frac{1}{x ^{4}} 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_{1}^{2} x^{2} d x + \int_{1}^{2} \frac{1}{x ^{4}} d x

\int_{1}^{2} x^{2} d x = \frac{7}{3}

\int_{1}^{2} \frac{1}{x ^{4}} d x = \frac{7}{24}

= \frac{7}{3} + \frac{7}{24}

化简

\frac{7}{3} + \frac{7}{24} : \frac{21}{8}

= \frac{21}{8}

\int_{3}^{4} \frac{2}{25 - x ^{2}} d x

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