Ask a Doubt
Request a call back

Join NOW to get access to exclusive study material for best results

ICSE Class 10 Answered

maths
question image
Asked by shaimaobaid30420 | 03 Nov, 2023, 02:20: PM
answered-by-expert Expert Answer
begin mathsize 14px style x space left parenthesis 1 minus y right parenthesis space d x space minus space left parenthesis space 1 minus space y squared right parenthesis left parenthesis x minus 1 right parenthesis d y space equals space 0 end style
 
Above expression is written as
 
begin mathsize 14px style fraction numerator d y over denominator d x end fraction space equals space fraction numerator x space left parenthesis space 1 minus space y right parenthesis over denominator left parenthesis 1 minus y squared right parenthesis left parenthesis x minus 1 right parenthesis end fraction space equals space fraction numerator x over denominator left parenthesis x minus 1 right parenthesis end fraction cross times fraction numerator 1 over denominator left parenthesis 1 plus y right parenthesis end fraction end style
 
begin mathsize 14px style left parenthesis 1 plus y right parenthesis space d y space equals space fraction numerator x over denominator open parentheses x minus 1 close parentheses end fraction space d x end style
 
begin mathsize 14px style left parenthesis 1 plus y right parenthesis space d y space equals space fraction numerator left parenthesis x minus 1 right parenthesis plus 1 over denominator open parentheses x minus 1 close parentheses end fraction space d x space end style
 
begin mathsize 14px style left parenthesis 1 plus y right parenthesis space d y space equals space space d x space plus space fraction numerator d x over denominator open parentheses x minus 1 close parentheses end fraction end style
By integrating both sides , we get
 
 
begin mathsize 14px style 1 half open parentheses 1 plus y close parentheses squared space equals space x space plus space log left parenthesis x minus 1 right parenthesis space plus space C open parentheses 1 plus y close parentheses squared space equals space 2 x space plus space 2 space log left parenthesis x minus 1 right parenthesis space equals space 2 x space plus space log left parenthesis x minus 1 right parenthesis squared space plus space C left parenthesis 1 plus y right parenthesis space equals space square root of 2 x space plus space log left parenthesis x minus 1 right parenthesis squared plus C end root space y space equals space square root of 2 x space plus space log left parenthesis x minus 1 right parenthesis squared plus C end root space minus space 1 space end style
Where C is constant of integration
-------------------------------------------------------------------
 
begin mathsize 14px style fraction numerator d y over denominator d x end fraction equals space square root of fraction numerator left parenthesis 1 minus y squared right parenthesis over denominator left parenthesis 1 minus x squared right parenthesis end fraction end root end style
begin mathsize 14px style fraction numerator d y over denominator square root of left parenthesis 1 minus y squared right parenthesis end root end fraction space equals space fraction numerator d x over denominator square root of left parenthesis 1 minus x squared right parenthesis end root end fraction end style
 
Let us use the following integration for above expression
 
Then we get
 
begin mathsize 14px style sin to the power of negative 1 end exponent y space equals space sin to the power of negative 1 end exponent x space plus space C y space equals space sin space left parenthesis space sin to the power of negative 1 end exponent x space plus space C space right parenthesis end style
 
Answered by Thiyagarajan K | 03 Nov, 2023, 03:37: PM

Application Videos

Concept Videos

Multiple Choice Questions Practice Test
Answered Unanswered My Questions My Answers
ICSE 10 - Maths
cot A - 1/ 2 - sec² = cot A / 1 + tan A
Asked by bhagvantingre | 24 Apr, 2024, 03:05: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
ICSE 10 - Maths
solve xdy-ydx=0
Asked by shaikafridi860 | 21 Apr, 2024, 11:22: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
ICSE 10 - Maths
if a is an acute angle and sec a = 17/8, find all other trigonometric rarios of angle a ( using trigonometric indentities).
Asked by aritramalakar4 | 13 Apr, 2024, 08:33: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
ICSE 10 - Maths
3√2x×x-5x-√2
question image
Asked by ashwanikaler9 | 11 Apr, 2024, 01:50: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
ICSE 10 - Maths
prove that
question image
Asked by botlarajshekhar | 22 Mar, 2024, 09:37: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
ICSE 10 - Maths
Mr. Gupta invested Rs. 33000 in buying Rs.100 shares of a company at 10% premium. The dividend declared by the company is 12% . Find: (a) the number of shares purchased by him. (b) his annual dividend
Asked by sagarmishra | 15 Mar, 2024, 03:22: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
ICSE 10 - Maths
 (a+b)²
Asked by dadoosumeksha | 13 Mar, 2024, 09:26: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
ICSE 10 - Maths
sheethal has a recurring deposit account in a bank and deposit rupees 300 and at rate of interest of 7℅ and recieved rupees 7725 on maturity, find the time which would the account will be held
Asked by jesnamariaroy2626 | 10 Mar, 2024, 11:28: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
ICSE 10 - Maths
if abc are in Continued proportion then prove that 3a2-4ab+5b2/3b2-4bc+5c2=a/c
Asked by vrj.parmar369 | 07 Mar, 2024, 11:27: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
ICSE 10 - Maths
sole
question image
Asked by ronaldlhouvum | 22 Feb, 2024, 02:42: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
My Class Videos Tests ₹ Plans Ask a Doubt
Get Latest Study Material for Academic year 24-25 Click here
×