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.
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, to the nearest thousandth, the area bounded by the curve , the -axis, and the line .
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 curve in the figure is .
What is the area of the shaded region? Give your answer exactly as a fraction.
The plan view of a single corridor floor is bounded by lines , and the curve , all measured in meters. What is the cost of covering 6 such corridors with granite at the price of 200 pounds per square meters?
Determine, to the nearest thousandth, the area of the region bounded by the graph of the function , where , and the lines and .