2508 Views

Evaluate double integral of (x^2+y^2)dxdy throughout the area enclosed by n the curves y=4x , x+3=3 , y=0 , y=2


ishitasharma23072003 11th Nov, 2020
Answer (1)
Subhrajit Mukherjee 12th Nov, 2020

Limiting value for x: x+3=3 => x=0 , x= y/4

Limiting value for y : y=0 , y=2

As the limiting value of x is dependent on y then we will integrate with respect to x then with respect to y.

Integrating with respect to x we get => [(x^3/3) + xy^2]

putting the limit of x=y/4 , x=0 we get: [(y^3/192)+(y^3/4)]

Now integrating with respect to y we get: [(1/192)+(1/4)] * (y^4/4)

Putting the limit y=2 , y=0 we get: [(1/192)+(1/4)] *4  => 49/48.

So the answer of the integration is 49/48.

I hope my answer helps you. All the very best for your future endeavors!


Related Questions

Chandigarh University Admissi...
Apply
Ranked #1 Among all Private Indian Universities in QS Asia Rankings 2025 | Scholarships worth 210 CR
TAPMI MBA 2025 | Technology M...
Apply
MBA Admission Open in Technology Management and AI & Data Science | NAAC A++ | Institution of Eminence | Assured Scholarships
Sanskriti University LLM Admi...
Apply
Best innovation and research-driven university of Uttar Pradesh
Maya Devi University LLM admi...
Apply
43.6 LPA Highest Package | 5.48 LPA Average Package | 150+ Courses in UG, PG, Ph.D
Amity University, Noida Law A...
Apply
700+ Campus placements at top national and global law firms, corporates, and judiciaries
Great Lakes PGPM & PGDM 2025
Apply
Admissions Open | Globally Recognized by AACSB (US) & AMBA (UK) | 17.3 LPA Avg. CTC for PGPM 2024 | Extended Application Deadline: 10th Feb 2024
View All Application Forms

Download the Careers360 App on your Android phone

Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile

150M+ Students
30,000+ Colleges
500+ Exams
1500+ E-books