integral from a to b of f(x)

解答

\int_{a}^{b} f (x) d x

\frac{f ( b ^{2} - a ^{2} )}{2}

求解步骤

\int_{a}^{b} f x d x

提出常数:

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

= f \cdot \int_{a}^{b} x d x

使用幂法则

= f [\frac{x ^{2}}{2}]_{a}^{b}

带入上下限计算后得:

\frac{b ^{2}}{2} - \frac{a ^{2}}{2}

= f (\frac{b ^{2}}{2} - \frac{a ^{2}}{2})

化简

= \frac{f ( b ^{2} - a ^{2} )}{2}

(ln (\frac{x}{4}))^{^{'}}

\int 2 x (2 - x) d x

d er i v a t i v e 3^{2^{x^{2}}}

x \to 0 lim (\frac{sin ( x ^{7} )}{x})

x \to - 2 + lim (\frac{- 1}{x ^{2} - 4})