finding the area under a curve using integration

FINDING THE AREA UNDER A CURVE

USING INTEGRATION

AS P1 MATH

BY: WILLIAM, VINCENT, WENDY

INTRODUCTION

• INTEGRATION IS ALSO CALLED ANTI-DIFFERENTIATION. THIS

MEANS THAT IT IS REVERSE DIFFERENTIATION.

• IF

THEN , WHERE .

EXAMPLE 1

• INTEGRATE:

• SOLUTION:

2 𝑥3−3 x+1

EXAMPLE 2

• INTEGRATE:

• SOLUTION: EXPAND

(2 𝑥−3 )2

DEFINITE INTEGRATION

• WHEN WE ARE GIVEN VALUES LIKE THIS: , WHERE A AND B ARE THE LIMITS OF THE INTEGRAL, THIS IS KNOWN AS DEFINITE INTEGRALS.

• EXAMPLE :

=

USE INTEGRATION TO FIND AREA

THE AREA UNDER A GRAPH CAN BE FOUND BY

USING THE FORMULA…

WHERE A IS THE LOWER LIMIT AND B IS THE

UPPER LIMIT.

EXAMPLE

• FIND THE AREA UNDER THE CURVE IN WHICH THE AREA IS BOUNDED BETWEEN X=2 AND X=6.

SOLUTION

X = 2 X = 6

AREA UNDER THE X-AXIS

• IF A CURVE LIES BELOW THE X-AXIS, THE AREA BETWEEN THAT PART AND THE X-AXIS IS

EXAMPLE

• THE CURVE MEET THE X-AXIS WHERE X=1 AND X=2.

FIND THE SHADED AREA.

SOLUTION

• WILL HAVE A NEGATIVE DOMAIN.

• REMEMBER

THIS IS THE AREA BELOW THE X-AXIS.

ANOTHER TYPE OF CURVE…

• IF A CURVE LIES PARTLY ABOVE AND PARTLY BELOW THE X-AXIS, THE TOTAL AREA WILL BE

AREA BETWEEN A CURVE AND THE Y-AXIS

• THE GRAPH SHOWS THE PART OF THE CURVE , FIND THE AREA OF THE SHADED REGION.

SOLUTION

• FIRSTLY, MAKE X THE SUBJECT OF THE EQUATION OF THE CURVE.

FIND THE AREA

QUESTION???