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...
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=...
Find the antiderivative: dy/dx = x - e^x. Find the antiderivative of f(t) = \frac{3}{t} - \frac{2}{t^2}. Find the Antiderivative of f(x) = \frac{8 - 5x^4 + 3x^7}{x^7}. Find an antiderivative F ( x ) with F' ( x ) = f ( x ) and F ( 0 ) = 5 . f ...
The function( F(x)) can be found by finding the indefinite integral of the derivative( f(x)). ( F(x)=∫ f(x)dx) Set up the integral to solve. ( F(x)=∫ e^(-x^2)dx) (∫ e^(-x^2)dx) is a special integral. The integral is the error function. ( (erf)(x)...
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} ...
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Therefore, the antiderivative of the original function is: ∫3x√1−9xdx=1ln(3)sin−1(3x)+C Conclusion The final answer can be expressed in logarithmic form: =log3(e)sin−1(3x)+C Show More | ShareSave Class 12MATHSINDEFINITE INTEGRALS ...
Find an antiderivative F(x) of f(x) = 11x - \sqrt x. Find the antiderivative for f(x) = \frac{2x^2 + x + 9}{(x - 1)(x^2 + 3)} Find the antiderivative f(x) = 2 x^{-4} for x > 0 Find an antiderivative F(x) with F'(x) = f(x) and F(0) = 0...
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. ...