Definite Integral - AP Calculus - Lecture Notes, Study notes of Calculus

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Calculus Section 4.3A Notes Learning Targets... 1. Represent an area under a curve using a definite integral 2. Use Geometry to evaluate a definite integral LT: Represent an area under a curve using a definite integral e Definition of a Definite Integral (on [a,bj)... n Bb A= lim > feo hee | rooax i=1 a nooo o Notice the similarity between summation and integral o f must be defined on [a,b] oa The limit must exist. If it exists, f is integrable. o a&bare the of integration, respectively « Miscellaneous (but significant) notes... o Adefinite integral is not the same thing as an indefinite integral; a definite integral is a & an indefinite integral is a . (Your calculator can do definite integrals, but not indefinite.) o Adefinite integral represents the Brea between the curve of the function & the x-axis. o Continuity implies integrability (if a function is continuous on [a,b], it is also integrable on [a,b] Set up, but do not evaluate, a definite integral that yields the area of the region. 1) fx) = 3; [0,5] £09 $ \ 3 dx | ° Slee lele cg 2) gy) = y3; [0,2] Le" Y Fy w SS ‘ ‘ 4 1 4 1/2