Integration by substitution and parts, and volumes of revolution (HL)

Learning objectives

Integrate the derivatives of tan x, sec x, cosec x, cot x, aˣ, logₐ x, arcsin x, arccos x and arctan x, including composites with a linear function, recognising standard forms such as 1/(a² + x²) and 1/√(a² − x²)

Use partial fractions to rewrite a rational integrand and then integrate it in terms of logarithms

Integrate by substitution, including substitutions that must be chosen and definite integrals in which the limits are changed

Integrate by parts, including repeated integration by parts, choosing which factor to differentiate

Find the area of a region enclosed by a curve and the y-axis over a given interval

Calculate volumes of revolution when a region bounded by a curve is rotated about the x-axis or the y-axis