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IntegrationQuestion and Answers: Page 23
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Question and Answers Forum |
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IntegrationQuestion and Answers: Page 23 |
| ∫_(1/2) ^2 ln(((ln(x+(1/x)))/(ln(x^2 −x+((17)/6)))))dx=? |
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| ∫_(−1) ^1 ∫_(−(√(1−y^2 ))) ^(√(1−y^2 )) ln (x^2 +y^2 +1)dx dy =? |
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| if x+ (1/x) = ϕ ( Golden ratio) ⇒ x^( 2000) + (1/x^( 2000) )=? |
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| Integrate ∫_0 ^1 Sin^2 (2Πx)dx |
| 1)∫^∞ _0 ((sin x)/(x^p +sin x))dx ,p>0 2)∫^∞ _π ((xcos x)/(x^p +x^q ))dx,p>0and q>0 3)∫^∞ _0 ((sin x^p )/( x^q ))dx, p>0,q>0 4)∫^2 _0 (dx/(∣ln x∣^p )) ,p>0 5)∫^1 _0 ((cos(1/(1−x)))/( ((1−x^2 ))^(1/n) ))dx 6)∫^∞ _0 (dx/(x^p ((sin^2 x))^(1/3) )) |
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| ∫^b _a (√((x−a)(b−x)))=¿ |
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| ∫^∞ _0 x^2 .e^(−x^2 ) dx=¿ |
| (((20)),(( 0)) ) (((10)),(( 1)) ) + (((20)),(( 1)) ) (((10)),(( 2)) ) +...+ ((( 20)),(( 9)) ) ((( 10)),(( 10)) ) =? |
| ∫_0 ^( 1) ∫_0 ^( 1) ((dxdy)/((1+xy )^( 4) ))=? |
| ∫ xe^(x^2 /2) dx |
| Ω= ∫_0 ^( ∞) e^( −x) cos(x)ln(x)dx=? −−− f (a )= ∫_0 ^( ∞) e^( −x) cos(x)x^( a) dx = Re ∫_0 ^( ∞) e^( −x) .e^( −ix) .x^( a) dx = Re ∫_0 ^( ∞) e^( −x (1+i)) .x^( a) dx = Re(L { x^( a) }∣_( s= i+1) ) = Re( ((Γ (1+a))/s^( a+1) ) ∣_( 1+i) = ((Γ (1+a))/((1+i)^( a+1) )) ) Re (Γ(1+a).2^( ((1+a)/2)) . e^( −((iπ)/4) (1+a)) ) Ω= f ′(0)=....... |
| Know: f(x)=3x+2+∫^1 _0 xf(x)dx Eluavte: ∫^2 _0 f(x)dx=¿ |
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| solve ∫t^(−6) (t^2 +3)^2 dt |
| prove Ω= ∫_0 ^(π/2) (( cos(x)+cos(5x))/(1+ 2sin(x))) =^( ?) (3/2) |
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