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Integration is the basic operation in integral calculus. While differentiation has straightforward rules by which the derivative of a complicated function ...

Basic Rules of Integration ; ax n dx = a, x · + C · x ; a dx = ax + C · x ; x dx = x · + C · x ; x 2 dx = x · + C · / ; 1, dx = ln (x) + C · e ...

Integral of A Function

Integration. Integration can be used to find areas, volumes, central points and many useful things. It is often used to find the area underneath the graph of a function and the x-axis.. The first rule to know is that integrals and derivatives …

Integration by Parts Recall the Product Rule: d dx [u(x)v(x)] = v(x) du dx + u(x) dv dx 2. Integrating both sides and solving for one of the integrals leads to our Integration by Parts formula: Z udv= uv Z vdu Integration by Parts (which I may abbreviate as IbP or IBP) \undoes" the Product Rule.

Integration Rules and Techniques Antiderivatives of Basic Functions Power Rule (Complete) Z xn dx= 8 >> < >>: xn+1 n+ 1 + C; if n6= 1 lnjxj+ C; if n= 1 Exponential Functions With base a: Z ax dx= ax ln(a) + C With base e, this becomes: Z ex dx= ex + C If we have base eand a linear function in the exponent, then Z eax+b dx= 1 a eax+b + C Trigonometric Functions Z

The sum rule of integration is: Integral of the sum of two functions is equal to the sum of integration of individual functions. ∫(f + g) dx = ...

Overview

The Indefinite Integral and Basic Rules of Integration ; Let a function be defined on some interval The function is called an antiderivative of if ; for all in ...

(This just means we find the antiderivative using IBP and then plug in the limits of integration the way we do with other definite integrals.) Trigonometric ...

Integration Rules of Basic Functions

Rules Function Integral; Multiplication by constant: ∫ cf(x) dx: c ∫ f(x) dx: Power Rule (n≠−1) ∫ x n dx: x n+1 n+1 + C: Sum Rule: ∫ (f + g) dx: ∫ f dx + ∫ g dx: Difference Rule: ∫ (f - g) dx: ∫ f dx - ∫ g dx: Integration by Parts: See Integration by Parts: Substitution Rule: See Integration by Substitution

There are certain rules defined for finding integrals. They include: Sum and Difference Rules: ∫ [f(x)+g(x)] dx = ∫ f(x) dx + ∫ g(x) dx; ∫ [f(x)-g(x)] dx = ...

Integration is the reverse of differentiation. However: If y = 2x + 3, dy/dx = 2. If y = 2x + 5, dy/dx = 2. If y = 2x, dy/dx = 2. So the integral of 2 can be 2x + 3, 2x + 5, 2x, etc. For this reason, when we integrate, we have to add a constant. So the integral of 2 is 2x + c, where c is a constant. A "S" shaped symbol is used to mean the ...

Integration Rules ; Square, ∫x2 dx, x3/3 + C ; Reciprocal, ∫(1/x) dx, ln|x| + C ; Exponential, ∫ex dx, ex + C ; ∫ax dx, ax/ln(a) + C.

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