Integration

Learning objectives

Integrate (ax + b)ⁿ for any rational n ≠ −1, together with sums and constant multiples, as the reverse process of differentiation

Find the equation of a curve from its gradient function dy/dx and one point on it by evaluating the constant of integration

Evaluate definite integrals, including simple improper integrals with an infinite limit or an integrand undefined at one limit, such as ∫₀⁴ x^(−½) dx or ∫₂^∞ x⁻³ dx

Use definite integration to find the area between a curve and the x-axis or the y-axis, between a curve and a straight line, and between two curves

Calculate volumes of revolution through 360° about the x-axis with π∫y² dx or about the y-axis with π∫x² dy, including regions that are not bounded by the axis of rotation