Calculus Early Transcendentals/ Ch.5

The Definitive Integral

a n∫ f(x)dx= lim Σ f(xk^*)Δx b n-->∞ k=1Δx = width of rectangle

the fundamental theorem of calculus

a ∫ f(x)dx= F(b)-F(a) b

Net Change Theorem

The definite integral of the rate of change of a quantity F'(x) gives the total change, or net change, in that quantity on the interval [a,b].

Integration by substitution

in integrating composite function, either using pattern recognition or change of variables to perform the integration

if f(x) has an anti derivative of F(X)...

then a ∫ f(x)dx= 1/k F(kx)+C b