# 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.

Q1:

The curve shown is . What is the area of the shaded region? Give an exact answer. • A
• B
• C1.584962501
• D0.4054651081
• E1.09861228866811

Q2:

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.

Q3:

The curve shown is . What is the area of the shaded region? Give an exact answer. • A1.09861228866811
• B
• C
• D
• E

Q4:

The figure shows the graph of . • A
• B
• C
• D
• E

Q5:

Determine the area of the plane region bounded by the curve and the lines , , and rounded to the nearest hundredth.

Q6:

The curve shown is . What is the area of the shaded region? Give an exact answer. • A1.09861228866811
• B
• C
• D
• E

Q7:

Let . Determine the area bounded by the curve , the -axis, and the two lines and .

• Asquare units
• Bsquare units
• Csquare units
• Dsquare units

Q8:

Determine the area of the plane region bounded by the curve and the -axis rounded to the nearest hundredth.

Q9:

The figure shows . • A
• B
• C
• D
• E

Q10:

Calculate the area of the plane region bounded by the curve and the -axis.

• A area units
• B area units
• C area units
• D area units

Q11:

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.

Q12:

Let . Determine, to the nearest thousandth, the area bounded by the curve , the -axis, and the line .

Q13:

Find the area of the region above the bounded by the curve and the lines and . Give an exact answer.

• A
• B
• C
• D
• E

Q14:

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. Q15:

The figure shows the graph of the function . Evaluate the area of the shaded region. Q16:

Find the area enclosed by the graph of , the , and the lines and .

• A18 square units
• B72 square units
• C36 square units
• D0 square units
• E9 square units

Q17:

Find the area of the shaded region. Q18:

The curve in the figure is . • A
• B
• C
• D
• E

Q19:

Determine, to the nearest thousandth, the area of the plane region bounded by the curve and the lines , , and .

Q20:

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?

Q21:

Determine, to the nearest thousandth, the area of the region bounded by the graph of the function , where , and the lines and .

Q22:

Determine the area of the plane region bounded by the curve , the -axis, and the two lines and .

• A square units
• B65 square units
• C square units
• D square units

Q23:

Calculate the area bounded by the graph of the function and the two coordinate axes.

• A square units
• B square units
• C square units
• D75 square units
• E square units