Evaluate {eq}\displaystyle \int\frac{x^2}{\sqrt{9-x^2}}dx {/eq}. Using Trigonometric Substitution: The integral involves a square root term {eq}\displaystyle \, \sqrt{9-x^2} {/eq}. So a trigonometric substitution using the sin function will simplify this integral. This will change...
20.$$ \int \frac { x } { \sqrt { 9 - x ^ { 2 } } } d x = \ldots A $$$ A . - \sqrt { 9 - x ^ { 2 } } + C D . x + \sqrt { 9 - x ^ { 2 } } + C $$$ B . \sqrt { 9 - x ^ { 2 } } + C E . 1 + \sqrt { 9 - x ...
【解析】 解令$$ x = 3 s e c t $$,则$$ d x = 3 s e c t \cdot \tan t d t . $$ $$ \int \frac { \sqrt { x ^ { 2 } - 9 } } { x } d x = \int \frac { 3 \tan t } { 3 s e c t } \cdot 3 s e c t \cdot \tan t d t = 3 \int \...
Integrate: \int x \sqrt{ 1 - x^2 }dx Integrate the following function. int x + 2 over sqrt 4 - x^2 dx Integrate: \int (\sqrt x+\frac{1}{x^4})dx Integrate the following: int 2 - 8x sqrt 9 - 4x2 dx Integrate the following. \int \sqrt x \times ln(x) dx Integrate: \...
Delphi 常用的几个数学函数 1 Power函数,求次方 定义:function Power(X,Y): (Same type as parameter); 说明:X可以是整型,也可以是实型;返回值实型例子: var i:integer; begin i := Power(2,3); { 8 }
Answer to: integrate the following. integral from \int_{\frac{2}{3} }^{0} \sqrt{ 4 - 9 x ^ 2}dx By signing up, you'll get thousands of...
( x , y ) | x ^ { 2 } + y ^ { 2 } \leq 9 $$,其曲顶柱体的形状为半径为3的上半球体,所以,由二重积分的几何意义,有$$ \int \int \int \sqrt { 9 - x ^ { 2 } - y ^ { 2 } } d \sigma = \frac { 1 } { 2 } \cdot \frac { 4 } { 3 } \pi 3...
【解析】 23.【精析 $$ \int _ { 0 } ^ { \frac { 1 } { 2 } } \frac { x } { \sqrt { 1 - x ^ { 2 } } } \arcsin r d x = - \int _ { 0 } ^ { \frac { 1 } { 2 } } \arcsin x d ( \sqrt { 1 - x ^ { 2 } } \\ = - \sqrt { ...
Answer to: Evaluate the integral. (Use C for the constant of integration.) \int \frac{1}{x^2 \sqrt{9-x^2}}dx By signing up, you'll get thousands...
{eq}\int {{x^n}} dx = \frac{{{x^{n + 1}}}{{n + 1}} + c , {/eq} where {eq}c {/eq} is arbitrary constant. Answer and Explanation: Solution (1): Let {eq}\displaystyle I_1 = \int \frac{\sqrt{x}-x^{\...