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In integral calculus, Euler's formula for complex numbers may be used to evaluate integrals involving trigonometric functions.Using Euler's formula, any trigonometric function may be written in terms of complex exponential functions, namely and and then integrated.
Note: x > 0 is assumed throughout this article, and the constant of integration is omitted for simplicity. Integrals involving only logarithmic functions [ edit ]
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In calculus, integration by parametric derivatives, also called parametric integration, [1] is a method which uses known Integrals to integrate derived functions. It is often used in Physics, and is similar to integration by substitution .
In calculus, the Leibniz integral rule for differentiation under the integral sign, named after Gottfried Wilhelm Leibniz, states that for an integral of the form () (,), where < (), < and the integrands are functions dependent on , the derivative of this integral is expressible as (() (,)) = (, ()) (, ()) + () (,) where the partial derivative indicates that inside the integral, only the ...
Connection with integration [ edit ] For a one-dimensional Riemann sum over domain [ a , b ] {\displaystyle [a,b]} , as the maximum size of a subinterval shrinks to zero (that is the limit of the norm of the subintervals goes to zero), some functions will have all Riemann sums converge to the same value.