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...Unit integral calculus structure introduction objectives antiderivatives basic definitions standard integrals algebra of methods integration by substitution parts rational functions some simple partial fraction decomposition irrational trigonometric definite fundamental theorem area function first second evaluation a properties applications summary answers to saqs in this we shall introduce the notions indefinite and various techniques will also cover which can be evaluated using these have seen that one problems motivated concept derivative was geometrical finding tangent curve at point similarly problem areas plane regions enclosed curves recently discovered egyptian manuscripts reveal formulas for triangles rectangles were known even bc could find any figure bounded straight line segments but no method figures had evolved till much later third century archimedes successful rigorously proving formula circle his solution contained seeds present day it only seventeenth newton leibniz a...