x Antiderivative In calculus, an antiderivative, primitive, or indefinite integral, is a mathematical technique for finding the family of functions whose derivative is a given function. In other words, an antiderivative is the original function of which the derivative was taken. The most common exam...
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=...
What is the antiderivative of {eq}\frac{(x^2 - 70)}{2} {/eq}? Sum And Difference Rule: The method for evaluating the integral of a function in which several small entities are included in sum and difference is known as the sum and difference rule. ...
Answer to: Find the Antiderivative of: \int \frac{1}{10 + x^{2} + 2x} By signing up, you'll get thousands of step-by-step solutions to your...
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试题来源: 解析 A 结果一 题目 What is the particular antiderivative of whose x-intercept is 3? ( ) A. B. C. D. 答案 A相关推荐 1What is the particular antiderivative of whose x-intercept is 3? ( ) A. B. C. D. 反馈 收藏 ...
Answer to: Find the antiderivative, F(x), with F'(x) = f(x) and F(0) = 1. f(x) = -7 x. By signing up, you'll get thousands of step-by-step...
Antiderivative of a function is obtained by integrating that function. 1. Simplify the function . 2. Integrate the function. 3. Use "C" as constant of integration. Answer and Explanation:1 Anti derivative ofx+7xis ∫x+7xdx {eq}\Rightarrow \int \frac {\sqrt x}{x}... ...
Question: Recall that sin(x2) has no antiderivative (in terms of elementary functions). In this problem you will approximate ∫01sin(x2)dx using Taylor series.(a) Write the Maclaurin series of sin(x) then substitute x2 for...
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 ...