Integration

Indefinite Integration and the Constant of IntegrationSign up

understand integration as the reverse of differentiation and use the notation ∫ f(x) dx, including the role of the constant of integration · be able to integrate x^n for n ≠ -1, including sums and constant multiples of such terms, and find a curve from its gradient function given a point

Definite Integration and Area Under a CurveSign up

be able to evaluate definite integrals and interpret them as signed areas between a curve and the x-axis · be able to find the area between a curve and the x-axis, including regions that cross the axis (treating sign appropriately)

Area Between a Curve and a Line and Between Two CurvesSign up

be able to find areas between two curves, between a curve and a line, or between a curve and the y-axis using definite integration

Volumes of RevolutionSign up

be able to find the volume of revolution generated by rotating a curve about the x-axis or the y-axis through 2π radians, using V = π ∫ y^2 dx or V = π ∫ x^2 dy