FP3.4 - Integration

Integration of hyperbolic functions and expressions involving them.

Use fp3.4.1 - integration of hyperbolic functions to connect the rule to the data and decision in the question.

This matters because fp3.4.1 - integration of hyperbolic functions determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply fp3.4.1 - integration of hyperbolic functions to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: FP3.4.1 - Integration of hyperbolic functions is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Integration of inverse trigonometric ∫ ∫ For example, arsinh x dx, arctan x dx. and hyperbolic functions.

Use fp3.4.2 - integration of inverse trigonometric to connect the rule to the data and decision in the question.

This matters because fp3.4.2 - integration of inverse trigonometric determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply fp3.4.2 - integration of inverse trigonometric to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: FP3.4.2 - Integration of inverse trigonometric is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Integration using hyperbolic and To include the integrals of trigonometric substitutions. 1 1 1 1,,, (a2 + x2) (a2 − x2) (a2 + x2) (x2 − a2).

Use fp3.4.3 - integration to connect the rule to the data and decision in the question.

This matters because fp3.4.3 - integration determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply fp3.4.3 - integration to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: FP3.4.3 - Integration is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Use of substitution for integrals In more complicated cases, substitutions will be given. involving quadratic surds.

Use fp3.4.4 - use of substitution for integrals to connect the rule to the data and decision in the question.

This matters because fp3.4.4 - use of substitution for integrals determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply fp3.4.4 - use of substitution for integrals to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: FP3.4.4 - Use of substitution for integrals is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Derive and use simple reduction formulae for integrals, including powers of sine.

Use fp3.4.5 - reduction formulae to connect the rule to the data and decision in the question.

This matters because fp3.4.5 - reduction formulae determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply fp3.4.5 - reduction formulae to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: use the formula and units given in the question, show the substitution and interpret the result; the calculation alone is not the conclusion.

The calculation of arc length and The equation of the curve may be given in cartesian or the area of a surface of revolution. parametric form.; Equations in polar form will not be set.

Use fp3.4.6 - the to connect the rule to the data and decision in the question.

This matters because fp3.4.6 - the determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply fp3.4.6 - the to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: FP3.4.6 - The is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.