# Case study Chapter 8 ( Application of integral )

Case study 4: Read the following and answer the question(Case study application of integral 4)

A boy design a pizza by cutting it with a knife on a card board. If pizza is circular in shape which is represented by the

equation and edge of knife represents a straight line given by . A boy design a pizza by cutting it with a knife on a card board. (i) Point of intersection of the line and pizza shown in figure is(are)

(a) (1, √3)                (b) (√3, 1) and (-√3, -1)

(c) (2, 0)                   (d) (2, 0) and (0, 0)

(ii) The area of piece OABO of a cicular design pizza is

(a) π sq.units             (b) 2π sq.units

(c) π/3 sq.units          (d) 2π/3 sq.units

(iii) The area of the piece OABCO of the circular designed pizza is

(a) π sq.units               (b) 2π sq.units

(c) 3π sq.units              (d) 4π sq.units

(iv) The area of semicircular shape of the pizza is

(a) π sq.units               (b) 2π sq.units

(c) 4π sq.units              (d) 8π sq.units

(v) Area of the whole pizza is (in sq. units)

(a) π                                (b) 2π

(c) 4π                              (d) 8π

We have ,

x² + y² = 4 —-(i)

and x = √3y —-(ii)

Solving (i) and (ii) we get,

3y² + y² = 4

⇒ 4y² = 4

⇒ y² = 1 ⇒ y = ±1

and x = ±√3

Point of intersection are (√3, 1) and (-√3, -1) Required area given by,     sq.units We have area of OABCO      sq.units Required area = 2×Area of OABCO square units

Area of whole pizza = 2× Area of semicicular shape  sq.units

## Some other Case study problem

Case study 1: Read the following and answer the question.(Case study application of integral 1)

Nowadays, almost every boat has a triangular sail. By using a triangular sail design it has become possible to travel against the wind using a technique known as tacking. Tacking allows the boat to travel forward with r
triangular sail on the walls and three edges(lines) at the triangular sail are given by the equation x = 0, y = 0 and y + 2x – 4 = 0 respectively.

Case study 2: Read the following and answer the question(Case study application of integral 2)

An architect designs a building whose lift (elevator ) is from outside of the building attached to the walls. The floor (base ) of the lift (elevator) is in semicircular shape. The floor of the elevator (lift) whose circular edge is given by the equation and the straight edge(line) is given by the equation y = 0. An architect designs a building whose lift (elevator ) is from outside

Case study 3: Read the following and answer the question(Case study application of integral 3)
A student designs an open air Honeybee nest on the branch of a tree, whose plane figure is parabolic and the branch of tree is given by a straight line. A student designs an open air Honeybee nest on the branch of a tree

Case study 5:-A farmer has a triangular shaped field. His, son a science student observes the triangular field has three edges and can be drawn on a plain paper with three lines given by its equations.(Case study application of integral 5)

Based on the above information answer the following question:

(i) Find the area of the shaped region in the figure shown below. (ii) Find the area of the triangle  ΔABC. Nisha and Arun appeared for first round of an competitive examination Owner of a whole sale computer shop plans to sell two type of computers – a desktop The equation of motion of a missile are x = 3t, y = -4t, z = t where the time

For more solution 