Get 2 FREE Instant-Explanations on Filo with code FILOAPP

Sketch the region lying in the first quadrant and bounded by y

Question

Sketch the region lying in the first quadrant and bounded by $y = 9 x^{2}$ , $x = 0$ , $y = 1$ and $y = 4$ . Find the area of the region, using integration.

Views: 748 students

Found 2 tutors discussing this question

Elizabeth Discussed

Sketch the region lying in the first quadrant and bounded by

y = 9 x^{2}

x = 0

y = 1

and

y = 4

. Find the area of the region, using integration.

13 mins ago

Discuss this question LIVE

13 mins ago

Text solutionVerified

Here,

x^{2} = \frac{y}{9}

is a upward parabola having its vertex at the origin and

y = 1, y = 4

are the lines which are parallel to

x -

axis at

y = 1

y = 4

unit distance from it

Similarly

x^{2} = \frac{y}{9}

has even power of

y

and is symmetrical about

y - a x i s

So the required area is written as

Required area

= \int_{1}^{4} x d y

= \int_{1}^{4} \frac{y}{3} d y

= \frac{1}{3} [\frac{y ^{3/2}}{3/2}]_{1}^{4}

= \frac{2}{9} [4^{3/2} - 1^{3/2}]

= \frac{2}{9} (8 - 1)

= \frac{14}{9}

sq. units.

Was this solution helpful?

150

Report

One destination to cover all your homework and assignment needs

Learn Practice Revision Succeed

Instant 1:1 help, 24x7

60, 000+ Expert tutors

Textbook solutions

Big idea maths, McGraw-Hill Education etc

Essay review

Get expert feedback on your essay

Schedule classes

High dosage tutoring from Dedicated 3 experts

Trusted by 4 million+ students

Stuck on the question or explanation?

Connect with our math tutors online and get step by step solution of this question.

231 students are taking LIVE classes

Question Text	Sketch the region lying in the first quadrant and bounded by $y = 9 x^{2}$ , $x = 0$ , $y = 1$ and $y = 4$ . Find the area of the region, using integration.
Answer Type	Text solution:1
Upvotes	150