WebApr 19, 2024 · Find the derivative of `e^(sqrt(x))` from the first principle. WebLet I = ∫ − ∞ ∞ e − x 2 d x. Then, I 2 = ( ∫ − ∞ ∞ e − x 2 d x) × ( ∫ − ∞ ∞ e − y 2 d y) = ∫ − ∞ ∞ ( ∫ − ∞ ∞ e − ( x 2 + y 2) d x) d y Next we change to polar form: x 2 + y 2 = r 2, d x d y = d A = r d θ d r. Therefore I 2 = ∬ e − ( r 2) r d θ d r = ∫ 0 2 π ( ∫ 0 ∞ r e − r 2 d r) d θ = 2 π ∫ 0 ∞ r e − r 2 d r
Find the derivative of `e^(sqrt(x))` from the first principle.
WebTo remove the radical on the left side of the equation, square both sides of the equation. √x+62 = (x−6)2 x + 6 2 = ( x - 6) 2 Simplify each side of the equation. Tap for more steps... x+6 = x2 −12x+36 x + 6 = x 2 - 12 x + 36 Solve for x x. Tap for more steps... x = 10,3 x = 10, 3 WebSymbolab is the best integral calculator solving indefinite integrals, definite integrals, improper integrals, double integrals, triple integrals, multiple integrals, antiderivatives, and more. Which is an antiderivative? An antiderivative of function f (x) is a function whose derivative is equal to f (x). Is integral the same as antiderivative? irs application for tax exempt status
Integration of Root x - Formula, Examples - Cuemath
WebOnline math solver with free step by step solutions to algebra, calculus, and other math problems. Get help on the web or with our math app. WebWhen you have multiple variables within the ln parentheses, you want to make e the base and everything else the exponent of e. Then you'll get ln and e next to each other and, as we know from the natural log rules, eln (x) =x. So, the equation becomes eln (5x-6) = e2 Since eln (x) = x, eln (5x-6) = 5x-6 Therefore 5 x -6= e2 WebThe integration of root x is nothing but the integral of square root x with respect to x which is given by ∫√x dx = (2/3) x 3/2 + C, where C is the constant of integration, ∫ denote the symbol of the integration and dx indicates the integral of square root x with respect to x. We can compute the integration of root x using the formula of integration ∫x n dx = x n+1 /(n + 1) + … irs application for stimulus check 2020