InterviewSolution
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InterviewSolution
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हल कीजिए- `sin ^(-1)((dy)/(dx))=x+y.` |
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Answer» यहाँ `sin ^(-1) ((dy)/(dx))=x+y` `implies (dy)/(dx) =sin (x+y)" "...(1)` माना `x+y=v" "...(2)` x के सापेक्ष अवकलन करने पर, `1+(dy)/(dx)=(dv)/(dx) ` `implies (dy)/(dx) =(dv)/(dx)-1" "...(3)` समी (1),(2) और (3) `(dv)/(dx) =1+sin v` `implies (dv)/(dx) =1+sin v` `implies(dv)/(1+sin v)=dx` समाकलन करने पर, `int(dv)/(1+sinv) =int dx` `=int ((1)/(1+sin v)xx (1-sin v)/(1-sin v))dv =x+C` `implies int (1- sin v)/(1-sin^(2)v)dv=x+C` `implies int (1- sin v)/(cos^(2)v)dv=x+C` `impliesint((1)/(cos ^(2)v)-(sin v)/(cos ^(2)v))dv=x+c` `impliesintsec^(2) vdv-int tan v sec vdv=x+C.` `impliestan v- sec v=x+C` `implies tan (x+y) -sec (x+y) =x+C.` |
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