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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 off(x)=2xx2+1. Integration: The antiderivative is the integration of the given function. The solution of the given indefinite integral can be obtained by using the substituting method. Answer and Explanation:1 The given function is: ...
Find the antiderivative of {eq}\int_{1}^{3}x^2dx {/eq} Integration: Consider a function {eq}\displaystyle f(x) {/eq} with upper limit {eq}\displaystyle b {/eq} and lower limit {eq}\displaystyle a {/eq} Then integral is written as {eq}\displaystyle \int _a^b f(x)dx {/eq...
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...
A natural logarithm is a logarithm of base {eq}e {/eq}, and it is customary to write a natural log as {eq}\ln(x) = y {/eq} instead of {eq}\log_ex = y {/eq}. In math, {eq}e {/eq} is Euler's constant or theexponential. It is an irrational number that equals approxima...
◻ ◻ ◻ Find the most general antiderivative of the functionh(x)=(4x4-7x5+12).Use an upper-caseCfor any arbitrary constants. H(x)= There are 2 steps to solve this one.
i) int(sin x+cos x) dx ii) int( cosec x... 03:41 Find the antiderivative F of f defined by f(x)=4 x^3-6, where F(0)=3 02:56 Find the antiderivative (or integral) of the following functions by th... 03:05 Find the antiderivative (or integral) of the following functions...
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)=∫ 2/x-x+√2dx) Split the single integral into multipleintegrals. (∫ 2/xdx+∫ -xdx+∫ √2dx) Since ( 2) i...
Tutor 5 (1) Extensive knowledge of physics and mathematics, patient and kind. See tutors like this I'm going to assume that the number after each "x" is an exponent. Going off that assumption, there is a common formula for the antiderivative (also called an integral) of xn, that be...