1.36: Area bounded by exponential curve and normal

0606/12/M/J/18 — Question 11 · 10 marks

The diagram shows the graph of the curve

y = \dfrac{\mathrm{e}^{4x} + 3}{8}

. The curve meets the

y

-axis at the point

A

. The normal to the curve at

A

meets the

x

-axis at the point

B

Find the area of the shaded region enclosed by the curve, the line

AB

and the line through

B

parallel to the

y

-axis. Give your answer in the form

\dfrac{\mathrm{e}}{a}

, where

a

is a constant. You must show all your working.

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