# 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. A student designs an open air Honeybee nest on the branch of a tree

(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) 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. An architect designs a building whose lift (elevator ) is from outside

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.

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. A veterinary doctor was examining a sick cat brought by a pet lover The equation of motion of a missile are x = 3t, y = -4t, z = t where the time A dealer Ramprakash residing in a rural area open a shop to start his bussiness. He wishes to purchase a number of 