integral from 0 to 50 of 9.8(500-10y)

解答

\int_{0}^{50} 9.8 (500 - 10 y) d y

122500

求解步骤

\int_{0}^{50} 9.8 (500 - 10 y) d y

提出常数:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 9.8 \cdot \int_{0}^{50} 500 - 10 y d y

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

= 9.8 (\int_{0}^{50} 500 d y - \int_{0}^{50} 10 y d y)

\int_{0}^{50} 500 d y = 25000

\int_{0}^{50} 10 y d y = 12500

= 9.8 (25000 - 12500)

化简

= 122500

\frac{\partial}{\partial t} (2 t)

t an g e n t f (x) = \frac{6}{4 x + 1}, at x = - 1

d er i v a t i v e 3 x^{5} - 3 x^{4} + x^{3}

d er i v a t i v e y = \frac{( x ^{3} )}{3 ^{x}}

a re a 5 x - x^{2}, y = 0