February/March 2026 Paper 22

2026 · 8 questions · 14 parts · 50 marks

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Context for question 7

It is given that

\int_{a}^{2 a} \frac{1}{4} e^{2 x} (2 + e^{- x}) d x = 50

, where

a

is a positive constant.

7(a)Antiderivatives Definite IntegralsHard5 marks

Show that

a = \frac{1}{4} ln (200 + e^{a})

Draw with the mouse or a finger.

7(b)Root Finding IterationMedium2 marks

Show by calculation that the value of

a

lies between 1.0 and 1.5.

Draw with the mouse or a finger.

7(c)Root Finding IterationMedium3 marks

Use an iterative formula, based on the equation in part (a), to find the value of

a

correct to 4 significant figures. Give the result of each iteration to 6 significant figures.

Draw with the mouse or a finger.