3.47: Tangent and exact area under a curve

0606/21/O/N/21 — Question 10 · 9 marks

3.47 diagram
The diagram shows part of the curve y=5x+2xx2y = 5x + \dfrac{2}{x} - x^{2}.
(a)
Find, in the form y=mx+cy = mx + c, the equation of the tangent to the curve at the point where x=1x = 1.
[5]
(b)
Find the exact area enclosed by the curve, the xx-axis, and the lines x=1x = 1 and x=3x = 3.
[4]