Q. 55.0( 1 Vote )

# Find the area of the region included between y2 = 9x and y = x

In y2 = 9x parabola it is not defined for negative values of x hence the parabola will be to the right of Y-axis passing through (0, 0)

And y = x is a straight line passing through origin

We have to find area between y2 = 9x and y = x shown below

To find intersection point of parabola and line solve parabola equation and line equation simultaneously

Put y = x in y2 = 9x

x2 = 9x

x = 9

Put x = 9 in y = x we get y = 9

Hence point of intersection is (9, 9)

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

Let us find area under parabola

y2 = 9x

y = 3√x

Integrate from 0 to 9

Now let us find area under straight line y = x

y = x

Integrate from 0 to 9

Using (i)

area between parabola and line = 54 – 40.5 = 13.5 unit2

Hence area bounded is 13.5 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
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
Application of Biotechnology48 mins
Interactive Quiz on Integration by Parts56 mins
Integration by Substitution56 mins
How to find Maxima & Minima?43 mins
Application of Nerst Equation20 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