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एक सतत वास्तविक फलन f सम्बन्ध f(2x) =3f...

एक सतत वास्तविक फलन f सम्बन्ध `f(2x) =3f( x) AA x in R ` को संतुष्ट करता है। यदि ` underset( 0)overset1 int f(x) dx =1 ` है, तो निश्चित समाकलन ` underset 1 overset2 int f(x) dx ` का मान ज्ञात कीजिए।

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The correct Answer is:
`5`
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BANSAL HINDI-INDEFENITE & DEFINITE INTEGRATION -EXERCISE -2 (SECTION -B (DEFINITE INTEGRATION ) )
  1. underset(1) overset( (1+ sqrt5)/(2))int (x^(2) +1)/( x^(4) -x^(2) +1) ...

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  2. निश्चित समाकलन underset0 overset pi int |sqrt2 sin x +2 cos x |dx क...

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  3. एक सतत वास्तविक फलन f सम्बन्ध f(2x) =3f( x) AA x in R को संतुष्ट करत...

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  4. माना Un = underset( 0)overset((pi)/(2))int sin ^(-1) ""(2x)/( 1+x^(2...

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  5. underset( 0)overset( sqrt3) int sin ^(-1) ""(2x)/( 1+x^(2)) dx

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  6. ( 5050 underset( 0)overset( 1) int (1- x^(50)) ^(100)dx)/( underset(0...

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  7. यदि underset( 0)overset(npi ) int (x | sin x| )/( 1+|cos x|) dx ( n ...

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  8. माना की 1= underset( 0)overset( 1)int (2+ 3x+4x^(2))/( 2sqrt(1+x+x^(2...

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  9. दर्शाये की दोनों समाकलन का योग underset(-4) overset(-5) int e^((x+5)^...

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  10. माना F(x) =max . (sin pix , cos pi x ) है,तो (pi)/(4sqrt2) underset...

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  11. underset( 0)overset( pi//2) int tan ^(-1) [(sqrt(1+sin x)+sqrt( 1-sin...

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  12. underset(-1) overset(1) int ((2x^(332)+x^(998) +4x ^(1668) sin x ^(691...

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  13. माना की I= underset(0) overset( pi//2) int (cos x +4) /( 3 sin x +4...

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  14. माना y= f(x) एक द्विघातीय फलन है जहाँ f'(2) =1 है , तो समाकलन unde...

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  15. माना की f(x)= {:{ ([ -1], if -2 le x le 0 ),( |x-1| , if 0lt xle 2 ...

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  16. फलन f(x) = {:{( underset( 0)overset( x )int (5+ 2|t-1|) dt , x gt 2 ),...

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  17. यदि y= x ^(underset( 1 )overset( x) int lnt dt ) है , तो (dy)/(dx)...

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  18. अचर 'a' (a gt 0 ) एवं 'b ' ज्ञात करों जो इस प्रकार है की underset(...

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  19. underset( x to infty ) Lim (d)/(dx) underset ( 2 sin ""(1)/(x))overse...

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  20. underset( 0 )overset( infty ) int (lnt )/(x^(2) +t^(2)) dt= ( piln 2...

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