1.15: Area between an exponential curve and a chord

0606/11/O/N/17 — Question 5 · 8 marks

The diagram shows part of the graph of

y = 4\mathrm{e}^{2x} + 16\mathrm{e}^{-2x}

meeting the

y

-axis at the point

A

and the line

x = 1

at the point

B

(i)

Find the coordinates of

A

[1]

(ii)

Find the

y

-coordinate of

B

[1]

(iii)

Find

\displaystyle\int (4\mathrm{e}^{2x} + 16\mathrm{e}^{-2x})\,\mathrm{d}x

[2]

(iv)

Hence find the area of the shaded region enclosed by the curve and the line

AB

. You must show all your working.

[4]