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IntegrationQuestion and Answers: Page 324 |
find the value of ∫_(−1) ^1 (dx/((√(1−x^2 )) +(√(1+x^2 )))) . |
find I= ∫_0 ^∝ ((cosx)/(cosh(x)))dx |
find I=∫_0 ^π (dx/(cosx +2sinx)) . |
find ∫∫_D (x+y)^2 e^(x^2 −y^2 ) dxdy with D={(x,y)∈R^(2 ) /0<x<1 and 0<y<1−x }. |
calculate in terms of x f(x)= ∫_0 ^(π/(2 )) (dt/(1+xsint)) . |
find the value of I= ∫_0 ^1 ((t−1)/(lnt))dt . |
find the value of I_a = ∫∫_D_a e^(−((x^2 +y^2 )/2)) dxdy with D_a ={(x,y)∈R^2 / x^2 +y^2 ≤ a^2 } |
∫3x^2 /x^6 +1 |
find the value of ∫_(2/π) ^(6/π) x^3 cos([(1/x)])dx |
xy=(1−x^2 )(dy/dx) x=0 y=1 |
xy=(1−x^2 )(dy/dx) x=0 y=1 |
∫_(1/8) ^(1/2) ⌊ln ⌈(1/x)⌉⌋ dx |
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find the value of ∫_0 ^( ∝) (dx/((x+1)(x+2)(x+3))) . |
let give D={( x,y )∈R^2 /x^2 −x +y^2 ≤ 4 and 0≤y≤1} calculate ∫∫_D ln(xy)(√( x^2 +y^2 dxdy )) |
give the decomposition of F(x) = (1/(x^(2n) +1)) inside C[x] then find the value of ∫_0 ^∞ (dx/(1+x^(2n) )) n∈N and n≠o |
prove that ∫_0 ^1 (dx/(x+ e^x )) = Σ_(n=0) ^∝ (((−1)^n )/((n+1)^(n+1) )) A_n with A_n = ∫_0 ^(n+1) t^n e^(−t) dt . |
find ∫ (dx/(x^6 −1)) . |
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∫_0 ^∞ (1/x^2 )dx |
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find the value of ∫_0 ^∞ e^(−px) /sinx/dx with p>0 |
find the value of ∫_0 ^(1 ) x E((1/x))dx |
let give Γ(x)= ∫_0 ^∞ t^(x−1) e^(−t) dt with x>0 prove that lim _(n−>∝) ∫_0 ^n (1−(t/n))^n t^(x−1) dt = Γ(x) |
let give Γ(x)= ∫_0 ^∞ t^(x−1) e^(−t) dt and x>0(gamma euler function) prove that Γ(x) =lim_(n−>∝) (((n!) n^x )/(n(n+1)(n+2)...(n+x))) |
Pg 319 Pg 320 Pg 321 Pg 322 Pg 323 Pg 324 Pg 325 Pg 326 Pg 327 Pg 328 |