Get 2 FREE Instant-Explanations on Filo with code FILOAPP

Using integration, find the area of the triangular region boun

Question

Using integration, find the area of the triangular region bounded by the lines $y = 2 x + 1, y = 3 x + 1$ and $x = 4$ .

Views: 756 students

Found 3 tutors discussing this question

Chloe Discussed

Using integration, find the area of the triangular region bounded by the lines

y = 2 x + 1, y = 3 x + 1

and

x = 4

10 mins ago

Discuss this question LIVE

10 mins ago

Text solutionVerified

y = 2 x + 1

is the line passing through

A (\frac{- 1}{2}, 0)

and

B (0, 1) .

y = 3 x + 1

is the line passing through

C (\frac{- 1}{3}, 0)

and

B (0, 1)

x = 4

is the line parallel to y-axis and passing through

D (4, 0) .

Required area

=

Area of

O D FB +

Area of

O D EB

= \int_{0}^{4} (3 x + 1) d x - \int_{0}^{4} (2 x + 1) d x

= [\frac{3 x ^{2}}{2} + x]_{0}^{4} - [\frac{2 x ^{2}}{2} + x]_{0}^{4}

= [\frac{3 ( 4 ) ^{2}}{2} + 4 - 0] - [\frac{2 ( 4 ) ^{2}}{2} + 4 - 0]

= 28 - 20

= 8

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	Using integration, find the area of the triangular region bounded by the lines $y = 2 x + 1, y = 3 x + 1$ and $x = 4$ .
Answer Type	Text solution:1
Upvotes	150