PRESENTATION 2 MATHEMATICS AREA

GROUP PRESENTATION
2

DBM20023: ENGINEERING MATHEMATICS
2

LECTURER NAME: MADAM JEYASRI A/P PACKIRYSAMY
STUDENTS NAME: NORSHAZLYANA BINTI ZAHARI
(15DKM21F1079)
KISHEN A/L SHANMUGA RAJU (15DKM21F1075)
CHANG YOU JING (15DKM21F1087)

INTRODUCTION

We can obtain the area between a curve, the x-axis, and specific ordinates (that is, values of
x), by using integration. We know this from the units on Integration as Summation, and on
Integration as the Reverse of Differentiation.

QUESTION NUMBER 5

The figure above shows a quadratic curve and a
straight line with respective equations.

= 2 + 2 + 2 and 7 − 2

The points A and B are the points of interaction
between the quadratic curve and the straight
line.

a) Find the coordinates of A and B.

a) Determine the exact area of the finite region

bounded by the quadratic curve and the
straight line, shown shaded in the above
figure.

HERE IS THE SOLUTION FOR THE QUESTION

a) = 2 + 2 + 2 = 7 − 2

= 2 + 2 + 2 = 7 − 2

= 2 + 2 − 7 + 2 + 2 = 0

= 2 − 5 + 4 = 0

− 4 , − 1

= 1, = 4

, = 7 1 − 2 , = 7 4 − 2

= 5 = 26

= 1,5 , = (4,26)

HERE IS THE SOLUTION FOR THE QUESTION

) 1 = (26 + 5) × 3 × 1

2

= 46.5

2 = 4 2 + 2 + 2
1

= ( 3 + 2 2 + 2 ) 4
2 1
3

= ( 3 + 2 + 2 ) 4
1
3

= [ 4 3 + 4)2 + 2 4 − [ 1 3 + 1 2 + 2 1 ]

33

= 42

Shaded Area = 93 − 42
2

= 4.5

CONCLUSION

A function and the equation for the area between its graph and the x-axis are related to each
other by the antiderivative. The Fundamental Theorem of Calculus enables us to evaluate
definite integrals. This empowers us to find the area between a curve and the x-axis.

THANK
YOU