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P= underset( 0)overset(infty )int (x^(2)...

` P= underset( 0)overset(infty )int (x^(2))/( 1+x^(4)) dx, Q= underset( 0)overset( infty ) int (x dx )/( 1+x^(4)) ` तथा ` R= underset( 0)overset(infty ) int (dx)/( 1+x^(4)) ` है , तो सिद्ध करों।
` Q= (pi)/(4).`

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BANSAL HINDI-INDEFENITE & DEFINITE INTEGRATION -EXERCISE -2 (SECTION -B (DEFINITE INTEGRATION ) )
  1. underset( 0)overset( pi//2) int e^(x) {cos (sin x) cos ^(2) ""(x)/(2)...

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  2. underset1 oversete int {(1+x )e^(x) +( 1-x) e^(-x) } ln x dx

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  3. P= underset( 0)overset(infty )int (x^(2))/( 1+x^(4)) dx, Q= underset(...

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  4. P= underset( 0)overset(infty )int (x^(2))/( 1+x^(4)) dx, Q= underset(...

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  5. P= underset( 0)overset(infty )int (x^(2))/( 1+x^(4)) dx, Q= underset(...

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  6. रूपांतरण विधि पर प्रश्न underset(0)overset(pi//2)int sqrt(1 + sin x)...

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  7. यदि निश्चित समाकलन 1= underset(0)overset( 2) int (3x^(2) -3x+ 1) cos ...

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  8. underset( -sqrt2)overset(sqrt2)int (2x^(7) +3x^(6) -10 x ^(5) -7x^(3) ...

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  9. a ge 2 के लिए यदि निश्चित समाकलन underset0 oversetinfty int (dx)/( a...

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  10. underset( -2)overset( 2)int (x^(2)- x)/( sqrt(x^(2) +4)) dx

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  11. u= underset( 0)overset( pi//4) int ((cos x )/( sin x +cos x) ) ^(2)...

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

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

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

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

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

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

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  18. ( 5050 underset( 0)overset( 1) int (1- x^(50)) ^(100)dx)/( underset(0...

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

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

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