Application of Integrals

Topics in this chapter

• Definite Integral Setup
• Area Under Curves
• Area Between Curves
• Area With Horizontal Strips
• Special-Function Curves
• Symmetry and Geometric Regions

Cheat sheet

Practice questions

1. Question 1Q-1EFA38

   Find the area bounded by the curve y = x, the x-axis, the y-axis, and the line x = 3.

   1. A.3 square units
   2. B.9/2 square units
   3. C.6 square units
   4. D.9 square units
   See the answer and solution
2. Question 2Q-553016

   The area enclosed between the curves y = 2x and y = x² is:

   1. A.1/3 square unit
   2. B.2/3 square unit
   3. C.4/3 square units
   4. D.8/3 square units
   See the answer and solution
3. Question 3Q-D1728A

   Find the area of the region bounded by the parabola y² = 4x and the line x = 1.

   1. A.2 square units
   2. B.8/3 square units
   3. C.4 square units
   4. D.16/3 square units
   See the answer and solution
4. Question 4Q-9F9449

   Using integration, find the area enclosed by the circle x² + y² = 9.

   See the answer and solution
5. Question 5Q-2199E1

   The area under the curve y = sin x and above the x-axis from x = 0 to x = π is:

   1. A.1 square unit
   2. B.2 square units
   3. C.π square units
   4. D.π/2 square units
   See the answer and solution