Since f(x)=\int xe^{-x^{2}}\d x, let u=-x^2, \d u=-2x\d x or \dfrac {-\d u}{2}=x\d x. Thus, f(x)=\int e^{u}\left(-\dfrac {\d u}{2}\right)=-\dfrac {1}{2}e^{u}+C=-\dfrac {1}{2}e^{-x^{2}}+C and f(0)=1 ⇒ - 12(e^0)+C=...
In summary, the conversation discusses the evaluation of the anti derivative of e^x^2 as a Taylor Series. The conversation also mentions the use of the formula \frac{f^(n)(a)}{n!}(x-a)^n and the importance of using parentheses when writing e^x^2 to avoid confusion. The individual...
antiderivative the antiderivative of a function f is any function f which is differentiab1e and satisfies f t f t at a11 points in the domain of f p 115Exponential growth Some biological systems can be modeled using the idea of exponential growth. This means the variable of interest, x, ...
Find the antiderivative F (x) of f (x) = x / {3 (12 x^2 - 6)}, given F (1) = 5. Find an antiderivative of f(x). Find the antiderivative of f(t) = \frac{3}{t} - \frac{2}{t^2}. Find the antiderivative of g(x) = -8e^{x + 4} - \frac{5}{x + 7} - 5...
Find the antiderivative of the function. f(x) = 7e^x a) e^{7x} b) \frac {1}{7}e^{7x} What is the integral to: \int \frac {2x^2 - 3x + 1}{x(x^2 - 1)(x - 2)^3(x^2 + 4)^2} dx Find the antiderivative of f(x) = fraction {1}{(2x+1)^3} ...
C′(x)=5x2−4x;C(0)=3,000Specific Antiderivatives:Whenever we find an antiderivative for a function, we can actually find an infinite amount of antiderivatives that will work. This is because there is always a general constant term in every antiderivative...
An antiderivative of f(x)=F(x) =int[log(logx)+(logx)^(-2)]dx+c =xlog(logx)-int(x)/(xlogx)dx+int(logx)^(-2)dx+c Integrating by parts in the first integral =xlog(logx)-[x(logx)^(-1)+int(logx)^(-2)dx]+int(logx)^(-2)dx+c [Again integrating by parts
Find the most general antiderivative of the function:(Check your answer by differentiation.) g (v) = 5 + 3 sec^2 v. What is the antiderivative of the function f(x) = tan^2 (x) + (2x - 3)^5? Find the general antiderivative of the given problem...
Since f(r) is decreasingf(z)=eFigure 6.4: An antiderivative F(r) ofFigure 6.3: Graph of f(r) = ef(x)=e^(-x^2)for positive r, we know that F(r) is concave down for positive r. Since f(r) 0 as r txthe graph of F(r) levels off at both ends See Figure 6.4. ...
We are exploring the antiderivative of the mathematical expression e√x / √x. By employing a variable substitution (u = √x), we can simplify the expression and find the derivative du/dx. Through a series of algebraic manipulations, we isolate dx and re