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  • Please solve RD Sharma Class 12 Chapter 20 Areas of Bounded Region Exercise 20.3 Question 8 Maths textbook solution.

Please solve RD Sharma Class 12 Chapter 20 Areas of Bounded Region Exercise 20.3 Question 8 Maths textbook solution.

Answers (1)

Answer:

8 sq units

Hint:

Given:

y=2x+1,y=3x+1 and x=4

Solution:

The given lines are

y=2x+1…..(1)

y=3x+1…..(2)

x=4…….(3)

https://www.sarthaks.com/?qa=blob&qa_blobid=1472378851162222032

For intersection points of (1) and( 3)

Y=2x4+1=9

Coordinates of intersecting point of 1 and 3 is (4,9) for intersection point of (2) and (3)

Y=3x4+1=13

i.e, coordinates of intersection point of (2) and (3) is (4, 3)

For intersection point of (1) and (2)

2x+1=3x+1=>x=0

Y=1

i.e., coordinates of intersection point of (1) and (2) is (0, 1)

Shaded region is required triangle region.

Required Area =Area of trapezium OABD-Area of trapezium OACD

\begin{aligned} &\int_{0}^{4}(3 x+1) d x-\int_{0}^{4}(2 x+1) d x \\ &=\left[3 \frac{x^{2}}{2}+x\right]_{0}^{4}-\left[\frac{2 x^{2}}{2}+x\right]_{0}^{4} \\ &=[(24+4)-0]-[(16+4)-0]=28-20 \end{aligned}

=8 sq units

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