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4 of 4 objectives have lessons · 0 studied · 0 secure
What Cambridge says you should be able to do, in our words. Codes are the topic number plus the objective’s position.
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.
Examples: ∫(2x³ − 5x + 1) dx and ∫ 1/(2x + 3)² dx.
Taught in: Integrating (ax + b)ⁿ, Integrating powers of x · 12 questions
Solve problems involving the evaluation of a constant of integration.
Example: find the equation of the curve through (1, −2) for which dy/dx = √(2x + 1).
Taught in: Finding a curve from its gradient · 5 questions
Evaluate definite integrals.
Includes simple cases of 'improper' integrals, such as the integral of x^(−½) from 0 to 1 and the integral of x^(−2) from 1 to ∞.
Taught in: Definite integrals, Improper integrals · 10 questions
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; and to find a volume of revolution about one of the axes.
A volume of revolution may involve a region that is not bounded by the axis of rotation, e.g. the region between y = 9 − x² and y = 5 rotated about the x-axis.
Taught in: Area between two graphs, Area under a curve, Volumes of revolution, Volumes with a hole · 21 questions