Integration
Reverse differentiation, evaluate exact or numerical integrals and choose the correct boundaries for non-negative regions.
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Before you begin
Reverse differentiation, evaluate exact or numerical integrals and choose the correct boundaries for non-negative regions.
Learning goals
- Find antiderivatives within the permitted scope
- Evaluate definite integrals
- Relate a definite integral to area under a curve
- Find complete power antiderivatives on the stated interval
- 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 a polynomial definite integral with linked exact working
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.
Lessons
Work through them in order.
About lesson progress
Lesson marks record what you have studied. Checks show understanding separately. Guest marks come from this device.
- Antiderivatives and positive areaRecover antiderivatives with their conditions, then select the correct boundaries and vertical separation for positive area.
- Exponential integrals and between-curve areasCheck inner factors, exact and numerical integrals, and changing upper/lower boundaries for regions on or above the axis.