LIVE Course for free

Rated by 1 million+ students
Get app now
0 votes
in Mathematics by (39.2k points)

Using integration, find the area of the region bounded by the line x - y + 2 = 0, the curve x = y and Y-axis.

1 Answer

+1 vote
by (30.5k points)
selected by
Best answer

Given curves are

x - y + 2 = 0, ...........(i)

the curve x = y ..........(ii)

Consider x = y  or x2 = y, which represents the parabola whose vertex is (0, 0) and axis is Y-axis.

Now, the point of intersection of Eqs. (i) and (ii) is given by

But x = - 1 does not satisfy the Eq. (ii)

x = 2

Now, putting x = 2 in Eq. (ii), we get

2 = y or y = 4

Hence, the point of intersection is (2,4).

But we have actual equation of parabola x = y, it means a semi-parabola which is one right side of Y-axis.

The graph of given curve area shown below :

Clearly, area of bounded region = Area of region OABO

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.