Writing equations in questions is problematic - some symbols regularly get eliminated.The integral of e to the power x is: e to the power x + C If your expression contains no variables, for example e times e, or e to the power e, then the entire expression is a constant; in this case, the integral is this constant times x + C.
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Given a wave f(x, t), we call period T the interval of time we need to wait before the form of the wave is repeated. Obviously, we must choose a constant x and observe the wave passing trough it.For exemple, for f(x, t) = ei(kx - wt) it's f(x, t + T) = ei(kx - w(t + T)), so that we have 0 = f(x, t + T) - f(x, t) = ei(kx - wt) (e-iwT - 1) → e-iwT = 1 → T = n 2π/w, with n element of Z. If we are considering two near peaks of f (that is a good way to define T) n = 1, and we have the famous T = 2π/w.
What do you mean? As this is a calculus question, I presume that you are asking for a derivative or integral The derivative of any function of the form ƒ(x) = a * x ^ n is ƒ'(x) = a * n * x ^ (n-1) The integral of any function of the form ∫ a*x ^ n is a / (n+1) * x ^ (n+1) + C Your function that you gave is 1 / x^(2) which is equal to: x^(-2) Thus the derivative is: -2 * x^(-3) And the integral is: -x^(-1) + C
Use integration by parts. integral of xe^xdx =xe^x-integral of e^xdx. This is xe^x-e^x +C. Check by differentiating. We get x(e^x)+e^x(1)-e^x, which equals xe^x. That's it!
Writing equations in questions is problematic - some symbols regularly get eliminated.The integral of e to the power x is: e to the power x + C If your expression contains no variables, for example e times e, or e to the power e, then the entire expression is a constant; in this case, the integral is this constant times x + C.
integral of e to the power -x is -e to the power -x
The integral of a single term of a polynomial, in the form of AxN is (A/N+1) x (N+1). The first integral of 2x is x2 + C. The second integral of 2x is the first integral of x2 + C, which is 1/3x3 + Cx + C.
For n not equal to -1, it is 1/(n+1)*xn+1 while for n = -1, it is ln(|x|), the logarithm to base e.
I'm not sure if you mean e^x + 17 or e^(x+17) so we'll do both. First, the integral of e^x + 17 because these terms are being added you can integrate them separately: integral((e^x)dx) + integral(17dx) integral of e^x is just e^x + C Integral of 17 is 17x + C, so we get: e^x + 17x + C Second, the integral of e^(x+17) we know how to integrate the form e^u, so just do a u substitution u=x+17 du=dx so we get integral((e^u)du)=e^u + C resubstitute for u and get e^(x+17) + C
x=1
The antiderivative, or indefinite integral, of ex, is ex + C.
H. E. Bethel has written: 'On the convergence and exactness of solutions of the laminar boundry-layer equations using the N- parameter integral formulation of Galerkin - Kantorovich - Dorodnitsyn'
(e^x)^8 can be written as e^(8*x), so the integral of e^(8*x) = (e^(8*x))/8 or e8x/ 8, then of course you have to add a constant, C.
A part of calculus is about limits derivate and integrals... so for example: lim((1+1/n)^n) (n->infinity) is e=2.17.... d/dx (e^-x^2) = -2xe^-x^2 integral(x^2+ln(x)) = (x^3)/3+1/x+c
maths signs
Given a wave f(x, t), we call period T the interval of time we need to wait before the form of the wave is repeated. Obviously, we must choose a constant x and observe the wave passing trough it.For exemple, for f(x, t) = ei(kx - wt) it's f(x, t + T) = ei(kx - w(t + T)), so that we have 0 = f(x, t + T) - f(x, t) = ei(kx - wt) (e-iwT - 1) → e-iwT = 1 → T = n 2π/w, with n element of Z. If we are considering two near peaks of f (that is a good way to define T) n = 1, and we have the famous T = 2π/w.