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Integration and applications of integration — Question 11

QCAA 2023, Paper 2 · 4 marks

Q11 · 2023 · Technology-activeSimple familiar4 marks

QUESTION 11 (4 marks)

The bounded region between the graphs of the functions y=−1+sec⁡(x5)y=-1+\sec\left(\frac{x}{5}\right) and y=0.1x2y=0.1x^2 over a certain domain is shaded as shown. The functions intersect at the origin and point A.
Shaded bounded region between y=-1+sec(x/5) and y=0.1x^2 with intersection A
a)
Determine the coordinates of point A.
[1 mark]
b)
Calculate the area of the shaded region.
[1 mark]
c)
The shaded region is rotated about the xx-axis to form a solid of revolution. Determine the volume of the solid formed.
[2 marks]
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