Q. 14

# Using integration, find the area of region bounded by the line y-1=x, the x-axis, and the ordinates x=-2 and x=3.

Given the boundaries of the area to be found are,

• The line equation is y = x +1

• The y= 0, x-axis

• x = -2 (a line parallel toy-axis)

• x = 3 (a line parallel toy-axis)

Thus the given boundaries are,

• The line y = x+1.

• x=-2 is parallel toy-axis at 2 units away from the y-axis.

• x=3 is parallel toy-axis at 3 units away from the y-axis.

• y = 0, the x-axis.

The four vertices of the region are,

Point A, where the line y = x+ and x=3 meet i.e. A(3,4).

Point B, where the line y = x +1 and x=-1 meet i.e.

B(-2,-1).

Point C, where the x-axis and x=-2 meet i.e. C (-2,0).

Point D, where the x-axis and x=3 meet i.e. D(3,0).

Area of the required region = Area of ABCD.

From (1) we can clearly say that, the area of ABCD has to be divided into twopieces i.e. area under CBE and ADE as the line equations changes the sign of x.

So the equation AB becomes negative between after it crosses the point E.

[Using the formula and ]

The Area of the required region = 8.5 sq. units.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Microsporogenesis & Megasporogenesis49 mins
Meselson and Stahl experiment49 mins
NEET 2021 | Transcription - An important Topic62 mins
DNA Fingerprinting42 mins
Interactive Quiz on Sexual Reproduction in flowering plants44 mins
Pedigree chart58 mins
MCQs of Ecology for NEET52 mins
Application of Biotechnology48 mins
Medelian disorder series: Thalassemia, Sickle cell anaemia & Phenylketonuria60 mins
Theories of origin of life in one go41 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses