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IntegrationQuestion and Answers: Page 312
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Question and Answers Forum |
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IntegrationQuestion and Answers: Page 312 |
| prove that ∫_0 ^∞ (e^(−t) /(√t))dt= e^(i(π/4)) ∫_0 ^∞ (e^(−ix) /(√x))dx. |
| find ∫_γ (e^z /(z(z+1)))dz with γ={z∈C/ ∣z−1∣=2} |
| find ∫_(−∞) ^(+∞) (dx/((1+x^2 )( 2+e^(ix) ))) . |
| find ∫_(−∞) ^(+∞) (x^2 /((x^2 +1)^2 (x^2 +2x+2)))dx. |
| find ∫_0 ^(2π) ((cos(2t))/(3−cost)) dt. |
| find A_n = ∫_(−∞) ^(+∞) (dx/((1+x^2 )^n )) with n from N and n≥1. |
| L means laplacr trsnsform find L (sin(at)) and L(cos(at)). |
| L means laplace transform find L(e^(at) )(s). |
| calculate ∫_γ (e^z /((z−1)(z+3)^2 ))dz with γ id the positif circle γ={z∈C/ ∣z∣=(3/2)}. |
| find ∫_0 ^∞ ((sin^2 (3x))/x^2 )dx. |
| let give 0<α<1 find in terms of α the value of integral ∫_0 ^∞ (dx/(x^α (1+x))) . |
| let give a>1 find ∫_0 ^(2π) (dt/(a+cost)) . |
| let give I_(m,a) =∫_0 ^∞ ((cos(mx))/((1+x^2 )(x^2 +a^2 )))dx 1)verify that I_(m,1) =lim_(a→1) I_(m,a) 2) find the value of ∫_0 ^∞ ((x sin(mx))/((1+x^2 )^2 ))dx |
| find F( (1/(1+x^4 ))) F means fourier transform. |
| find the value of∫_(−∞) ^(+∞) ((x^2 −1)/(x^2 +1)) ((sinx)/x)dx. |
| find ∫_(−∞) ^(+∞) ((cosx)/(e^x +e^(−x) ))dx. |
| find the value of∫_0 ^∞ (x^3 /(1+x^7 ))dx. |
| 1) prove that ∀ x≥0 x −(x^2 /2)≤ln(1+x)≤x 2) find lim_(n→+∞) Π_(k=1) ^n (1 + (1/(k^2 +n^2 )))^n . |
| find I = ∫_0 ^(2π) ln(x−e^(iθ) )dθ and xfromR and x^2 ≠1. |
| find I_n = ∫_0 ^π (dx/(1+cos^2 (nx))) with n∈ N^★ . |
| find ∫ arcsin((√(x/(x+2))))dx. |
| find ∫ (x/(cos^2 x))dx. |
| find ∫_(−1) ^1 (dt/(t +(√(1+t^2 )))) . |
| find ∫_0 ^(π/2) cost ln(tant)dt. |
| find ∫_0 ^∞ (dt/((1+t^2 )^4 )) |
| find ∫_(−π) ^π ((2dt)/(2+sint +cost)) . |
Pg 307 Pg 308 Pg 309 Pg 310 Pg 311 Pg 312 Pg 313 Pg 314 Pg 315 Pg 316 |