In this lesson, we will learn how to calculate the areas of enclosed regions between a given curve and the x-axis as well as between specified bounds.

Q1:

A glassed, arched entry to a hotel follows the curve π¦ = β 1 2 ( π₯ β 9 ) ( π₯ β 3 ) , where π¦ is the vertical height of the arch at a distance of π₯ metres from the floor. If glass costs 1β190 LE per square metre, calculate the cost of the entrance.

Q2:

Determine the area of the plane region bounded by the curve π¦ = 8 π₯ 4 and the lines π₯ = 1 , π₯ = 8 , and π¦ = 0 rounded to the nearest hundredth.

Q3:

The curve shown is π¦ = 1 π₯ . What is the area of the shaded region? Give an exact answer.

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