# Lesson Worksheet: Area between a Curve and a Line Mathematics • Higher Education

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:

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

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

Q2:

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

Q3:

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

Q4:

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

Q5:

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

Q6:

Find the area of the shaded region. Q7:

The figure shows the graph of the function . Evaluate the area of the shaded region. Q8:

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

Q9:

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

Q10:

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

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