What you’ll learn4 learning objectivesChoose one objective for a focused lesson, or study the complete topic.1.8.1Basic integration• understand integration as the reverse process of differentiation, and integrate (ax + b)n (for any rational n except -1), together with constant multiples, sums and differences e.g. xx x25 1 d3 - +;^h, x x23 1 d2+> ^h.Syllabus objective1.8.2Constant of integration• solve problems involving the evaluation of a constant of integration e.g. to find the equation of the curve through (1, -2) for which d d 21.x y x=+Syllabus objective1.8.3Definite integrals• evaluate definite integrals Including simple cases of 'improper' integrals, such as dxx 0 1 2 1- $ and 3 dxx2- 1;.Syllabus objective1.8.4Area and volume• use definite integration to find - the area of a region bounded by a curve and lines parallel to the axes, or between a curve and a line or between two curves - a volume of revolution about one of the axes. A volume of revolution may involve a region not bounded by the axis of rotation, e.g. the region between y = 9 - x2 and y = 5 rotated about the x-axis.Syllabus objective