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underset(1) overset( (1+ sqrt5)/(2))int ...

` underset(1) overset( (1+ sqrt5)/(2))int (x^(2) +1)/( x^(4) -x^(2) +1) ln (1+x-(1)/(x))dx `

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The correct Answer is:
` (pi)/(8) ln 2 `
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BANSAL HINDI-INDEFENITE & DEFINITE INTEGRATION -EXERCISE -2 (SECTION -B (DEFINITE INTEGRATION ) )
  1. u= underset( 0)overset( pi//4) int ((cos x )/( sin x +cos x) ) ^(2)...

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

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  3. underset(1) overset( (1+ sqrt5)/(2))int (x^(2) +1)/( x^(4) -x^(2) +1) ...

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

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

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

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

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  8. ( 5050 underset( 0)overset( 1) int (1- x^(50)) ^(100)dx)/( underset(0...

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

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

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

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

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

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

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

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

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

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

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

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

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