finding the area under a curve using integration
TRANSCRIPT
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???