NettetDerivadas Aplicaciones de la derivada Limites Integrales Aplicaciones de la integral Aproximación integral Series EDO Cálculo multivariable Transformada de Laplace … Nettet3 Find the integral: ∫ x 4 − x 2 d x = ∫ x 2 2 − x 2 d x using ∫ 1 a 2 − x 2 d x = arcsin ( x / a) + C I get x 2 2 arcsin ( x 2) + C. I'm not sure if the x 2 2 is right. Any suggestions and help would be great. calculus integration Share Cite Follow edited May 17, 2012 at 23:23 user17762 asked May 17, 2012 at 23:18 dave5678 181 2 3 8 Add a comment
Integration of the Square Root of a^2+x^2 eMathZone
NettetSolution Verified by Toppr Substituting u= ax in the integral ∫ x 2+a 2dx. Hence it can be written as a1∫ u 2+1du = a1tan −1u. ∫ u 2+1du =tan −1u (Standard integral formula) ∫ x … Nettet18. apr. 2024 · For the integral involving the root sqrt (x^2-a^2), we use the substitution: x=asectheta dx=asecthetatanthetad theta So, we get int (cancelacancelsecthetatanthetasqrt (a^2 (sec^2theta-1)))/ (cancelacancelsectheta))d theta Recalling the identity sec^2theta-1=tan^2theta, we get intatanthetasqrt … bak garanti
How do you integrate dx/ sqrt(x^2 - a^2)? Socratic
NettetIn this tutorial we shall find the integral of 1 over a^2-x^2. The integration is of the form. ∫ 1 a2– x2dx = 1 2aln(a + x a– x) + c. Now we have an integral to evaluate, I = ∫ 1 a2– x2dx ⇒ I = ∫ 1 (a– x)(a + x)dx ⇒ I = 1 2a∫[(a– x) + (a + x)] (a– x)(a + x) dx ⇒ ∫ dx a2– x2 = 1 2a[∫ 1 a + xdx + ∫ 1 a– xdx ... NettetIn calculus, an antiderivative, inverse derivative, primitive function, primitive integral or indefinite integral of a function f is a differentiable function F whose derivative is equal to the original function f.This can be stated symbolically as F' = f. The process of solving for antiderivatives is called antidifferentiation (or indefinite integration), and its opposite … bak games