Q. 14

Using integration, find the area of the region bounded by the line 2y = 5x + 7, x - axis the lines x = 2 and x = 8.

Answer :

Given equations are:

2y = 5x + 7 ...... (1)


x = 2 ...... (2)


x = 8 ...... (3)


Equation (1) represents line passing through and . Equation (2), (3) shows line parallel to y - axis passing through (2,0), (8,0) respectively.


A rough sketch of curves is as below:


12.PNG


We have to find the area of shaded region.


Required area


= (shaded region ABCDA)


(the area can be found by taking a small slice in each region of width Δx, then the area of that sliced part will be yΔx as it is a rectangle and then integrating it to get the area of the whole region)


(As x is between (2,8) and the value of y varies)


(as )




Now integrating by applying power rule, we get



Now applying the limits we get





Hence the area of the region bounded by the line 2y = 5x + 7, x - axis the lines x = 2 and x = 8 is equal to 96 square units.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Microsporogenesis & MegasporogenesisMicrosporogenesis & MegasporogenesisMicrosporogenesis & Megasporogenesis49 mins
Meselson and Stahl experimentMeselson and Stahl experimentMeselson and Stahl experiment49 mins
NEET 2021 | Transcription - An important TopicNEET 2021 | Transcription - An important TopicNEET 2021 | Transcription - An important Topic62 mins
DNA FingerprintingDNA FingerprintingDNA Fingerprinting42 mins
Interactive Quiz on Sexual Reproduction in flowering plantsInteractive Quiz on Sexual Reproduction in flowering plantsInteractive Quiz on Sexual Reproduction in flowering plants44 mins
Pedigree chartPedigree chartPedigree chart58 mins
MCQs of Ecology for NEETMCQs of Ecology for NEETMCQs of Ecology for NEET52 mins
Different high order thinking questions based on DNA structureDifferent high order thinking questions based on DNA structureDifferent high order thinking questions based on DNA structure39 mins
Medelian disorder series: Thalassemia, Sickle cell anaemia & PhenylketonuriaMedelian disorder series: Thalassemia, Sickle cell anaemia & PhenylketonuriaMedelian disorder series: Thalassemia, Sickle cell anaemia & Phenylketonuria60 mins
Application of BiotechnologyApplication of BiotechnologyApplication of Biotechnology48 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses