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•use a table of derivatives, or a table of anti-derivatives, in order to integrate simple func-tions. Contents 1. Introduction 2 2. Integrating powers 3 3. Integrating exponentials 3 4. Integrating trigonmetric functions 4 5. Integrals giving rise to inverse trigonometric functions 5 www.mathcentre.ac.uk 1 c mathcentre 2009
In the video, we work out the antiderivatives of the four remaining trig functions. Depending upon your instructor, you may be expected to memorize these antiderivatives. The antiderivatives of tangent and cotangent are easy to compute, but not so much secant and cosecant.
Table of antiderivatives I skip +Cin the right-hand expression Powers and logarithms xa 8 <: 1 a+1 xa+1 a6= 1 logjxj a= 1 x logx ( +1+1) 1x+1 logx ( +1) 2x Exponents e xe ax (loga) 1ax xex (x 1)ex e xe Trigonometric functions cosx sinx sinx cosx tanx logjcosxj cotx logjsinxj sec2 x tanx csc2 x cotx Hyperbolic functions coshx sinhx sinhx coshx ...
• use a table of derivatives, or a table of anti-derivatives, in order to integrate simple func-tions. Contents 1. Introduction 2 2. Integrating powers 3 3. Integrating exponentials 3 4. Integrating trigonmetric functions 4 5. Integrals giving rise to inverse trigonometric functions 5 1 c mathcentre July 20, 2005
The antiderivative of a function f f is a function with a derivative f. f. Why are we interested in antiderivatives? The need for antiderivatives arises in many situations, and we look at various examples throughout the remainder of the text.
3 Definition of the Integral as an Anti-Derivative If d dx (F(x)) = f(x) then f(x)dx = F(x). In words, If the derivative of F(x)isf(x), then we say that an indefinite integral of f(x) with respect to x is F(x). For example, since the derivative (with respect to x)ofx2 is 2x, we can say that an indefinite integral of 2x is x2. In symbols: d ...
Worksheet # 23: Antiderivatives. 1. Find the most general antiderivative for each of the following functions. 2. Find the values of the parameter A and B so that. (a) F(x) = (Ax + B)ex is an antiderivative of f(x) = xex. (b) H(x) = e2x(A cos x + B sin x) is an antiderivative of h(x) = e2x sin x. 3.
