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Integrals of Trigonometric Functions. ∫ sin x dx = − cos x + C. ∫ cos x dx = sin x + C. ∫ tan x dx = ln sec x + C. ∫ sec x dx = ln tan x + sec x + C. ∫ 1. sin. 2. x dx = ( x − sin x cos x ) + C.
Page 2 of 6. INTEGRATION FORMULAE STANDARD INTEGRALS 1. ∫, ( )- ( ) , ( )- [where, n ≠ 1- 2. ∫ ( ) ( ) * ( )+ 3. ∫ ( ) ∫ ( ) [where, v be the function of x]
Basic Integration Formulas. As with differentiation, there are two types of formulas, formulas for the integrals of specific functions and structural type formulas. Each formula for the derivative of a specific function corresponds to a formula for the derivative of an elementary function.
Sometimes we can rewrite an integral to match it to a standard form. More often however, we will need more advanced techniques for solving integrals. First, let’s look at some examples of our known methods. Basic integration formulas. 1. k dx = kx + C. xn+1. 2. xndx = + C. + 1. 3. dx = ln |x| + C. x. 4. ex dx = ex + C. 5. axdx ax. = + C ln(a)
Basic Integration Formulas. Power functions: xn+1. xn = + C, n 6= −1. + 1. 1. dx = ln |x| + C. x. 2. Trigonometric functions: Z. (3) sin xdx = − cos x + C. Z. (4) cos xdx = sin x + C. Z. (5) sec2xdx = tan x + C. Z. (6) csc2 xdx = − cot x + C. Z. (7) sec x tan xdx = sec x + C. Z. (8) csc x cot x = − csc x + C. 3. Exponential function: Z.
Mean Value Theorem for Integration Z b a f(x)dx = c)(b a), where 2[a;b] Average Value of a Function on [a;b] f(c) = 1 b a Z b a f(x)dx Substitution Method for Integration Let u = g (), then du dx 0)du dx, Z b a f(g x)) 0)dx Z a u du Z g( ) g(a) f(u)du Numerical Integration Midpoint Rule: f( x)dx ˇ Xn i=1 x i+ x 1 2 Trapezoidal Rule: Z b a f(x ...
This section introduces basic formulas of integration of elementary functions and the main properties of indefinite integrals. The section explains how to derive integration formulas from well-known differentiation rules.
