# Case study Chapter 8 (Application of integral )

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.

(i) Point of intersection of the parabola and straight line are

(a) (4, 0) and (-4, 0)           (b) (4, -4) and (4, 0)

(c) (-4, 4) and (4, 4)            (d) (2, 4) and (-2, 4)

(ii) Length of each horizontal strip of the bounded region is given by

(a)                    (b)

(c)                    (d)

(iii) Length of each vertical strip is given by

(a)     (b)

(c) 4                                           (d) None of these

(iv) Area of region bounded by parabola and line y = 4 is (in square units)

(a)                 (b) 32/3

(c) 64/3                                   (d) 128/3

(v) Area of each vertical strip is given by

(a)                           (b)

(c)                 (d)

Solution: (i) Answer (c)

Given equation of parabola is

x² = 4 y  —–(i)

And equation of straight line y = 4

∴ From (i), we get

x² = 4×4 = 16

⇒ x = ± 4

∴ Point of intersection are (4, 4) and (-4, 4)

We have,

x² = 4 y  —(i)

⇒ x = 2√y

Length of horizontal strip be = 2×2√y = 4√y

We have,

Length of vertical strip

We have,

Area of required bounded region

.

sq.units

Area of each(one) vertical strip

= y dx

## 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.

Case study 4: Read the following and answer the question

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 .

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.