integral from 1 to 16 of (x-3)/(sqrt(x))

解答

\int_{1}^{16} \frac{x - 3}{x} d x

24

求解步骤

\int_{1}^{16} \frac{x - 3}{x} d x

乘开

\frac{x - 3}{x} : x - \frac{3}{x}

= \int_{1}^{16} x - \frac{3}{x} 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}^{16} x d x - \int_{1}^{16} \frac{3}{x} d x

\int_{1}^{16} x d x = 42

\int_{1}^{16} \frac{3}{x} d x = 18

= 42 - 18

化简

= 24

y^{^{'}} = 1 + 4 y^{2}

t an g e n t f (x) = \frac{6 x}{x + 5}, at x = - 3

\frac{d}{d t} (3 t^{3} + s + 3 s^{3} + t)

\int (1 + x + x^{2} + x^{3}) d x

\int \frac{( 5 x ^{2} - 12 )}{( x ^{2} - 6 x + 13 ) ^{2}} d x