# Case study application of integral 2 chapter 8 class 12

# Case study Chapter 8 (Application of Integral)

**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.

**(i) Region bounded by the circular edge and the straight edge(line) has points of intersection as**

(a) (-2, 0) and (2, 0) (b) (0, 2) and (0, -2)

(c) (0, 0) and (4, 0) (d) (-4, 0) and (4, 0)

**(ii) Length of each vertical strip of the region bounded by the given curves is given by**

(a) (b)

(c) (d)

**(iii) The area of vertical strip between given circular edge and stright edge, is given by**

(a) (b)

(c) (d)

**(iv) The area of horizontal strip between given circular strip and the straight edge, is given by**

(a) (b)

(c) (d)

**(v) The area of the region of the floor of the lift of the building is (in square units)**

(a) (b)

(c) (d)

**Solution: (i) Answer(a)**

Given curve for circle and straight line are

x² + y² = 4 ——-(i)

y = 0 ———(ii)

∴ From (i) and (ii) we have

x² = 4 ⇒ x = ±2

∴ Points of intersection are (2, 0) and (-2, 0)

**(ii) Answer (c)**

Given curve , is circle whose equation is

x² + y² = 4 ——-(i)

It is a circle

y² = 4 – x² ⇒ y = √(4 – x²)

and y = 0 —–(ii)

it represents x – axis

Length of vertical strip is

y = √(4 – x²)

**(iii) Answer (b)**

We have

Area of one vertical strip

= y.dx = √(4 – x²).dx

**(iv) Answer (b)**

We have

Area of hozontal strip

= x.dy

= √(4 – y²).dy

**(v) Answer (c)**

We have

Area of the floor

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.

**Solution:** For whole question and solution click here

**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.

**Solution:** For solution click here

**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 .

**Solution:** For solution click here

**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.**

**Solution:** For solution click here