Worksheet: Area between a Curve and a Line
In this worksheet, we will practice applying integration to find the area between the curve of a function and a horizontal or vertical straight line.
A glassed, arched entry to a hotel follows the curve , where is the vertical height of the arch at a horizontal distance of meters from a point on the floor. If glass costs 1,190 LE per square meter, calculate the cost of the entrance.
The curve shown is . What is the area of the shaded region? Give an exact answer.
Determine the area of the plane region bounded by the curve and the -axis rounded to the nearest hundredth.
Find the area of the region above the -axis that is bounded by the graph of the function and the line . Give your answer to two decimal places.
Let . Determine the area bounded by the curve , the -axis, and the line .
Find the area of the region above the bounded by the curve and the lines and . Give an exact answer.
The figure shows the curve , which has a horizontal tangent at the point . Find the shaded area bounded by the curve and the horizontal tangent. Give your answer to 1 decimal place.
The figure shows the graph of the function . Evaluate the area of the shaded region.