Integration (Pure 3)

You will be able to

• Calculate an estimate of a definite integral by the trapezium rule, with the y-values to 5 d.p. and the estimate to 3 s.f.
• Predict from a sketch whether the trapezium rule gives an over-estimate or an under-estimate, and explain it from the tops of the trapezia.
• Describe how the error changes as the number of strips increases, and explain why a curve that changes curvature cannot be decided from the sketch.

You will be able to

• Determine which method an integral needs: a standard result, f′/f, parts, a given substitution, partial fractions or a trigonometric identity.
• Calculate an integral by parts, choosing u so that the new integral is simpler, and explain why the other choice makes it worse.
• Calculate definite integrals by a given substitution (changing the limits), by f′/f and by partial fractions, and indefinite integrals with + c.
• Explain how differentiating an answer checks it, and why a missing factor or a lost minus sign fails the check.