Page 106 - DMTH202_BASIC_MATHEMATICS_II

Unit 7: Definite Integral Applications

14. The three major steps to technique for identifying the area within two or more curves are Notes
graphing the two or more equations, finding out the points of..............................., and Setting
up and assessing the definite integral.
15. The curves are graphed to recognize which curve was the ............................... curve, and
which one was the lower curve.

7.3 Summary

 Applications of the definite integral include finding the area under simple curve and
finding the area within two curves.

 A straight line, y = const, above a distance in x is a rectangle and the area of a rectangle is
the height multiplied by the width.
 We have an estimation method that can be executed out to any extent of correctness as
long as we are enthusiastic to make the comprehensive computations.
 The rectangles can be created in a numerous methods, inside the curve, outside the curve
or by means of a mid-value.
 In definite practice the integrals are frequently mentioned not as 0 to x but as from a lower
limit to a higher limit corresponding to the area preferred.

 The technique for identifying the area within two or more curves is an imperative
application of integral calculus.
 Identifying the area within two or more curves allows us identify the area of irregular
shapes by assessing the definite integral.
 There are three major steps to this procedure: Graph the two or more equations, Find out
the points of intersection, and Set up and assess the definite integral.

7.4 Keyword

Estimation Approach: We have an estimation approach that can be executed out to any extent of
correctness as long as we are enthusiastic to make the comprehensive computations.

7.5 Review Questions

1. Illustrate the application of finding the area Under Simple Curve with example.

2. Exemplify the application of finding the area within two curves with example.
3. Find the area of the region bounded by y = 2x, y = 0, x = 0 and x = 2.
4. Find the area bounded by y = x , x = 0 and y = 3.
3
2
2
5. Find the area bounded by the curves y = x + 5x and y = 3 – x .
6. Find the area bounded by the curves y = x , y = 2 – x and y = 1.
2
2
2
7. Find the area of the region enclosed between the curves y = x - 2x + 2 and -x + 6 .
8. Find the area of the region enclosed by y = (x–1) 2 + 3 and y = 7.
3
9. Find the area of the region bounded by x = 0 on the left, x = 2 on the right, y = x above and
y = – 1 below.

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