# Find the area of the region bounded by the curves y2 = 9x, y = 3x.

y2 = 9x is the equation of a parabola and y = 3x is a straight line passing through origin

let us first roughly draw those equations

In y2 = 9x negative values of x are not allowed hence the graph is on right of X-axis that is the parabola opening to the right

To find point of intersection solve both the equations simultaneously

Put y = 3x in y2 = 9x

(3x)2 = 9x

9x2 = 9x

x2 – x = 0

x(x – 1) = 0

x = 0 and x = 1

Put x = 1 and x = 0 in y = 3x we will get y = 3 and y = 0 respectively hence the parabola and straight line intersect at (1, 3) and (0, 0)

We have to find the area between parabola and straight line

That area will be the area under parabola minus the area under the straight line from x = 0 to x = 1 as shown in figure below

area between parabola and straight line = area under parabola – area under straight line …(i)

Let us calculate the area under parabola

y2 = 9x

y = 3√x

Integrate from 0 to 1

Now let us calculate area under the line y = 3x that is area of triangle OAB

y = 3x

Integrate from 0 to 1

Using (i)

area between parabola and straight line = 2 – = 1/2 unit2

Hence area of the region bounded by the curves y2 = 9x and y = 3x is 1/2 unit2

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Fundamental Integration Formula59 mins
Application of Biotechnology48 mins
Interactive Quiz on Integration by Substitution47 mins
Lecture on Integration by parts55 mins
Lecture on some forms of integration54 mins
Lecture on integration by partial fractions62 mins
Interactive Quiz on Integration by Parts56 mins
Integration by Substitution56 mins
How to find Maxima & Minima?43 mins
Tangent & Normal To A Curve53 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