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Integration Formulas 1. Common Integrals Indefinite Integral Method of substitution ... Math Integration Formulas Keywords: Integrals Integration Formulas Rational Function Exponential Logarithmic Trigonometry Math Created Date: 1/31/2010 1:24:36 AM ...
FUNDAMENTAL THEOREM OF CALCULUS If f is a continuous function on the closed interval [a, b] and F is any antiderivative of f, then f(x)dx a ∫b =F(x) a b=F(b)−F(a) whereF $(x)=f(x) Average Value Of A Continuous Function f Over [a, b] Average Value = € 1 b−a f(x)dx a ∫b
8.If f is an even function, then Z a a f(x)dx = 2 Z a 0 f(x)dx 9.If f is an odd function, then Z a a f(x)dx = 0 Fundamental Theorem of Calculus I (FTC I) Z b a f(x)dx = F(b) F(a) Fundamental Theorem of Calculus II (FTC II) d dx Z x a f(t)dt = f(x) d dx Z u a f(t)dt = f(u)u0(with chain rule) Mean Value Theorem for Integration Z b a f(x)dx = c)(b ...
First, let’s look at some examples of our known methods. √ dx. cos(x) sin(2x) + sin(x) cos(2x) dx. f(x)g(x) dx. It is useful when one of the functions (f(x) or g(x)) can be differentiated repeatedly and the other function can be integrated repeatedly without difficulty. The following are two such integrals: x2exdx.
Use double angle and/or half angle formulas to reduce the integral into a form that can be integrated. Trig Formulas : sin ( 2. n odd. Strip 1 tangent and 1 secant out and convert the rest to secants using tan 2 x = sec 2 x - 1 , then use the substitution. = sec x . m even. Strip 2 secants out and convert rest to tangents using sec 2 x = 1 + tan.
Integration by parts (IBP) can be used to tackle products of functions, but not just any product. Suppose we have an integral Z f (x) g (x) dx. in mind.
Basic Integration Formulas 1. Power functions: (1) Z xn = xn+1 n+1 +C,n 6= −1 (2) Z 1 x dx = ln|x|+C 2. Trigonometric functions: (3) Z sinxdx = −cosx+C (4) Z cosxdx = sinx+C (5) Z sec2xdx = tanx+C (6) Z csc2 xdx = −cotx+C (7) Z secxtanxdx = secx+C (8) Z cscxcotx = −cscx+C 3. Exponential function: (9) Z exdx = ex +C 4. Inverse of ...
