SPECIALIST MATHS Calculus Week 6 Definite Integrals & Areas

Definite Integrals If is a continuous function for and The Fundamental Theorem of Calculus

What happened to the constant c

Definitions The function is called the integrand and are called the lower and upper bounds is the indefinite integral is called the definite integral

Properties of Definite Integrals

Example 22 Evaluate

Solution 22 Evaluate

Graphics Calculator for Example 1 RUN OPTNF4 (calc) F4 SHIFT SETUPArrow down to ANGLE F2(Rad)EXIT Ans = (CASSIO)

Example 23

Solution 23

Solution 23 (cont)

Solution 23 (continued)

Area Determination If is a positive continuous function in the interval then the shaded area is given by y x

Area for function that is also negative y x

Example 24

Solution 24 Find the area between the curve and the x-axis for Step 1 draw the curve on graphics calculator and find the x intercepts y x

Solution 24 continued Step 2 state the area relation Step 3 calculate definite integral either with G Calc or algebraically

Area between two curves y y

Example 25

Solution 25 Find the area between Step 1 draw the graph. y x

Solution 25 continued Step 2 find the points of intersection

Solution 25 continued Step 3 state the definite integral for the area and calculate it

This Week Text Book Pages 258 to 263 Exercise 7D3 Q 1 – 2 Exercise 7D4 Q 1 – 6 Exercise 7D5 Q 1 – 3 Questions 5 & 6 from Review Sets 6A – 6C Review Sets 7A – 7D