Take Class 12 Tuition from the Best Tutors
Affordable fees 1-1 or Group class Flexible Timings Verified Tutors Search in
Find the area enclosed by the parabola 4y = 3x2 and the line 2y = 3x + 12
Asked by Akhileshwar Last Modified
Answer 
Azhar M
The area enclosed between the parabola, 4y = 3x2, and the line, 2y = 3x + 12, is represented by the shaded area OBAO as
The points of intersection of the given curves are A (–2, 3) and (4, 12).
We draw AC and BD perpendicular to x-axis.
∴ Area OBAO = Area CDBA – (Area ODBO + Area OACO)
Let, f(x):2Y=3X+12 ,
Y=(3X+12)/2 implies equation 1.
,g(x):4Y=3X^2 ,
Then,Y=(3X^2)/4 implies equation 2.
By comparing eq.1 and eq.2,we get
(3X^2)/4=(3X+12)/2
Then do cross multiplication,i .e.
2×(3X^2)=4×(3X+12)
6X^2=12X+48
6X^2-12X-48=0
6(X^2-2X-8)=0
X^2-2X-8=0 implies equation 3.
X^2-4X+2X-8=0
X(X-4)+2(X-4)=0
(X-4)(X+2)=0
X= 4 or -2.implies eq.4.
Putting this value in eq.1&eq.2,we have
Y=3 or 12. Implies eq.5.
Area covered by parabola and line will be=
\int [f(x)-g(x)]dx from limit a to b
=\int [(3X+12)/2]dx - \int [(3X^2)/4]dx
=[(3X^2)/4+(6X)-(3X^3)/12] from limit -2 to 4
On applying limit,we get
Area=[1/2(24+48-6+24)-1/4(64+8)]
Area=[1/2(90)-1/4(72)]
Area=45-18= 27 sq.units
View 1 more Answers
Now ask question in any of the 1000+ Categories, and get Answers from Tutors and Trainers on UrbanPro.com
Ask a QuestionRecommended Articles
Meet Raghunandan.G.H, a B. Tech Tutor from...
Raghunandan is a passionate teacher with a decade of teaching experience. Being a skilled trainer with extensive knowledge, he provides high-quality BTech, Class 10 and Class 12 tuition classes. His methods of teaching with real-time examples makes difficult topics simple to understand. He explains every concept in-detail...
Read full article >
Meet Swati, a Hindi Tutor from Bangalore
Swati is a renowned Hindi tutor with 7 years of experience in teaching. She conducts classes for various students ranging from class 6- class 12 and also BA students. Having pursued her education at Madras University where she did her Masters in Hindi, Swati knows her way around students. She believes that each student...
Read full article >
Meet Sandhya R, a B.Sc tutor from Bangalore
Sandhya is a proactive educationalist. She conducts classes for CBSE, PUC, ICSE, I.B. and IGCSE. Having a 6-year experience in teaching, she connects with her students and provides tutoring as per their understanding. She mentors her students personally and strives them to achieve their goals with ease. Being an enthusiastic...
Read full article >
Meet Mohammad Wazid, a skilled trainer for...
Mohammad Wazid is a certified professional tutor for class 11 students. He has 6 years of teaching experience which he couples with an energetic attitude and a vision of making any subject easy for the students. Over the years he has developed skills with a capability of understanding the requirements of the students. This...
Read full article >
Looking for Class 12 Tuition ?
Learn from the Best Tutors on UrbanPro
Are you a Tutor or Training Institute?
Join UrbanPro Today to find students near youThe best tutors for Class 12 Tuition Classes are on UrbanPro
The best Tutors for Class 12 Tuition Classes are on UrbanPro
