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Question 26 (OR 1
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Find the area bounded by the curves y = √x, 2y + 3 = x and x axis

Last updated at Dec. 13, 2018 by Teachoo

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Question 26 (OR 1
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Find the area bounded by the curves y = √x, 2y + 3 = x and x axis

Transcript

Question 26 (OR 1st question) Find the area bounded by the curves y = βπ₯, 2y + 3 = x and x axis Given equation of curves y = βπ₯ 2y + 3 = x Here, y = βπ₯ y2 = x So, it is a parabola, with only positive values of y Drawing figure Drawing line 2y + 3 = x on the graph Finding point of intersection of line and curve y = βπ₯ Putting x = 2y + 3 from equation of line y = β(2π¦+3) Squaring both sides y2 = (β(2π¦+3))^2 y2 = 2y + 3 y2 β 2y β 3 = 0 y2 β 3y + y β 3 = 0 y(y β 3) + 1(y β 3) = 0 (y β 3) (y + 1) = 0 So, y = 3, y = β1 Since y cannot be negative y = 3 Since y cannot be negative y = 3 Now, putting y = 3 in lineβs equation 2y + 3 = x 2(3) + 3 = x 6 + 3 = x 9 = x x = 9 So, point is (9, 3) Now, letβs find the area Area required Area required = Area OAC β Area ABC Area OAC Area OAC = β«1_0^9βγπ¦ ππ₯γ y β Equation of curve y = βπ₯ Therefore, Area OAC = β«1_0^9βγβπ₯ ππ₯γ = β«1_0^9βγπ₯^(1/2) ππ₯γ = [π₯^(3/2)/(3/2)]_0^9 = 2/3 [9^(3/2)β0^(3/2) ] = 2/3 Γ 9^(3/2) = 2/3 Γ 3^((2 Γ 3/2) ) = 2/3 Γ 3^3 = 2 Γ 32 = 18 Area ABC Area ABC = β«1_3^9βγπ¦ ππ₯γ y β Equation of line 2y + 3 = x 2y = x β 3 y = π₯/2 β 3/2 Area ABC = β«1_3^9βγ(π₯/2β3/2) ππ₯γ = β«1_3^9βγπ₯/2 ππ₯γ β β«1_3^9βγ3/2 ππ₯γ = [π₯^2/(2 Γ 2)]_3^9 β 3/2 [π₯]_3^9 = [π₯^2/4]_3^9 β 3/2 [π₯]_3^9 = [9^2/4β3^2/4] β 3/2 [9β3] = [(81 β 9)/4] β 3/2 [6] = 18 β 9 = 9 Therefore, Area required = Area OAC β Area ABC = 18 β 9 = 9 square units

CBSE Class 12 Sample Paper for 2019 Boards

Paper Summary

Question 1

Question 2

Question 3

Question 4 (Or 1st)

Question 4 (Or 2nd)

Question 5

Question 6

Question 7

Question 8 (Or 1st)

Question 8 (Or 2nd)

Question 9

Question 10 (Or 1st)

Question 10 (Or 2nd)

Question 11

Question 12 (Or 1st)

Question 12 (Or 2nd)

Question 13 (Or 1st)

Question 13 (Or 2nd)

Question 14

Question 15

Question 16 (Or 1st)

Question 16 (Or 2nd)

Question 17

Question 18

Question 19

Question 20

Question 21 (Or 1st)

Question 21 (Or 2nd)

Question 22

Question 23

Question 24 (Or 1st)

Question 24 (Or 2nd)

Question 25

Question 26 (Or 1st) You are here

Question 26 (Or 2nd)

Question 27 (Or 1st)

Question 27 (Or 2nd)

Question 28

Question 29

Class 12

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About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.