Integration

• Integration by tabular integration, also known as integration by parts, is a method used to find the antiderivative of a product of two functions by applying the product rule in reverse.
• To find the area under a curve, we need to know its derivative.
• If f(x) is continuous on [a,b], then the definite integral exists and can be found using anti-differentiation (integrating).
• The definite integral represents the net signed area between the graph of a function and the x-axis over an interval.
• The formula for integration by parts is u(x)v'(x)-u'(x)v(x), where u(x) is an integrable function and v(x) is its derivative.
• If F(x) is an antiderivative of f(x), then ∫f(x)dx = F(b)-F(a)
• Integration by substitution is a technique where an integral is evaluated by substituting another expression for one of the variables and then integrating more easily.
• The power rule states that if f(x) = x^n then ∫x^nf(x)dx = (x^(n+1))/(n+1) + C.
• To use the product rule, take the derivative of one term using the power rule, then multiply it by the other term.