About this topic
Before you begin
Reverse differentiation, evaluate exact or numerical integrals and choose the correct boundaries for non-negative regions.
Learning goals
- Model and evaluate a nonnegative polynomial curve–line region with vertical strips
- Find complete power antiderivatives on the stated interval
- Evaluate a polynomial definite integral with linked exact working
- Find antiderivatives within the permitted scope
- Evaluate definite integrals
- Relate a definite integral to area under a curve
- Model and evaluate a nonnegative region between polynomial curves with vertical strips
- Find complete logarithmic antiderivatives on the stated interval
- Find complete exponential antiderivatives on the stated interval
- Find complete mixed antiderivatives on the stated interval
- Evaluate definite integrals of powers, reciprocals and exponentials exactly
Syllabus statements covered
- Include: integration as the reverse of differentiation; integration of x^n for any rational n and e^x, with constant multiples, sums and differences; integration of (ax + b)^n for any rational n and e^(ax+b); definite integral as area under a curve; evaluation of definite integrals; areas bounded by a curve and lines parallel to coordinate axes, between a curve and a line, or between two curves; approximating a definite integral using a graphing calculator or graphing software. Exclude: definite integral as a limit of sum; trapezium rule; area below the x-axis.
- Include: integration as the reverse of differentiation; integration of x^n for any rational n and e^x, with constant multiples, sums and differences; integration of (ax + b)^n for any rational n and e^(ax+b); definite integral as area under a curve; evaluation of definite integrals; areas bounded by a curve and lines parallel to coordinate axes, between a curve and a line, or between two curves; approximating a definite integral using a graphing calculator or graphing software. Exclude: definite integral as a limit of sum; trapezium rule; area below the x-axis.
Choose a lesson
Work through them in order.
- Not startedAntiderivatives and positive areaNextRecover antiderivatives with their conditions, then select the correct boundaries and vertical separation for positive area.
- Not startedExponential integrals and between-curve areasNextCheck inner factors, exact and numerical integrals, and changing upper/lower boundaries for regions on or above the axis.