Integration | OCR A A-Level Maths | 40 Worked Examples (H240)

40 fully worked integration questions for OCR A A-Level Mathematics (H240, spec 1.08a-g), every line explained and annotated to the real OCR M/A/B/SC mark scheme. Covers the core of integration: the fundamental theorem of calculus and the constant of integration, integrating x to a rational power including negative and fractional powers, the standard functions e to the kx, 1/x giving ln|x|, sin kx and cos kx, and the essential rewrite-first techniques OCR expects (expanding brackets, splitting a fraction over a single-term denominator, turning surds and reciprocals into powers). Includes finding the equation of a curve from its gradient function and a point, integrating twice from a second derivative, using the double-angle identities to integrate sin squared x and cos squared x, evaluating definite integrals, finding the area between a curve and the x-axis including regions below the axis where the signed integral must be made positive, and the area between two curves or a curve and a line. Features the OCR ‘show detailed reasoning’ style, the 3 significant figure and exact-answer conventions, and a key-facts reference box (OCR prints none of the basic integration table). Note: integration by substitution, integration by parts and integration using partial fractions are covered in separate packs, and volumes of revolution are not on the OCR H240 specification. Progressive difficulty from Easy to Challenging. Ideal for revision, homework and cover lessons.