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IntegrationQuestion and Answers: Page 324

Question Number 27215    Answers: 1   Comments: 0

find the value of ∫_(−1) ^1 (dx/((√(1−x^2 )) +(√(1+x^2 )))) .

findthevalueof11dx1x2+1+x2.

Question Number 27187    Answers: 0   Comments: 1

find I= ∫_0 ^∝ ((cosx)/(cosh(x)))dx

findI=0cosxcosh(x)dx

Question Number 27186    Answers: 1   Comments: 1

find I=∫_0 ^π (dx/(cosx +2sinx)) .

findI=0πdxcosx+2sinx.

Question Number 27185    Answers: 0   Comments: 0

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 }.

findD(x+y)2ex2y2dxdywithD={(x,y)R2/0<x<1and0<y<1x}.

Question Number 27184    Answers: 0   Comments: 1

calculate in terms of x f(x)= ∫_0 ^(π/(2 )) (dt/(1+xsint)) .

calculateintermsofxf(x)=0π2dt1+xsint.

Question Number 27183    Answers: 1   Comments: 0

find the value of I= ∫_0 ^1 ((t−1)/(lnt))dt .

findthevalueofI=01t1lntdt.

Question Number 27182    Answers: 0   Comments: 1

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 }

findthevalueofIa=Daex2+y22dxdywithDa={(x,y)R2/x2+y2a2}

Question Number 27083    Answers: 1   Comments: 0

∫3x^2 /x^6 +1

3x2/x6+1

Question Number 27045    Answers: 0   Comments: 0

find the value of ∫_(2/π) ^(6/π) x^3 cos([(1/x)])dx

findthevalueof2π6πx3cos([1x])dx

Question Number 27032    Answers: 0   Comments: 1

xy=(1−x^2 )(dy/dx) x=0 y=1

xy=(1x2)dydxx=0y=1

Question Number 27031    Answers: 1   Comments: 0

xy=(1−x^2 )(dy/dx) x=0 y=1

xy=(1x2)dydxx=0y=1

Question Number 27003    Answers: 0   Comments: 2

∫_(1/8) ^(1/2) ⌊ln ⌈(1/x)⌉⌋ dx

1/21/8ln1xdx

Question Number 26993    Answers: 0   Comments: 5

Question Number 26781    Answers: 1   Comments: 4

Question Number 26759    Answers: 1   Comments: 1

find the value of ∫_0 ^( ∝) (dx/((x+1)(x+2)(x+3))) .

findthevalueof0dx(x+1)(x+2)(x+3).

Question Number 26758    Answers: 0   Comments: 1

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 ))

letgiveD={(x,y)R2/x2x+y24and0y1}calculateDln(xy)x2+y2dxdy

Question Number 26757    Answers: 0   Comments: 3

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

givethedecompositionofF(x)=1x2n+1insideC[x]thenfindthevalueof0dx1+x2nnNandno

Question Number 26756    Answers: 0   Comments: 2

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 .

provethat01dxx+ex=n=0(1)n(n+1)n+1AnwithAn=0n+1tnetdt.

Question Number 26755    Answers: 1   Comments: 0

find ∫ (dx/(x^6 −1)) .

finddxx61.

Question Number 26738    Answers: 1   Comments: 1

Question Number 26631    Answers: 0   Comments: 1

∫_0 ^∞ (1/x^2 )dx

01x2dx

Question Number 26626    Answers: 1   Comments: 0

Question Number 26570    Answers: 0   Comments: 1

find the value of ∫_0 ^∞ e^(−px) /sinx/dx with p>0

findthevalueof0epx/sinx/dxwithp>0

Question Number 26569    Answers: 0   Comments: 1

find the value of ∫_0 ^(1 ) x E((1/x))dx

findthevalueof01xE(1x)dx

Question Number 26566    Answers: 0   Comments: 1

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)

letgiveΓ(x)=0tx1etdtwithx>0provethatlimn>∝0n(1tn)ntx1dt=Γ(x)

Question Number 26564    Answers: 0   Comments: 0

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)))

letgiveΓ(x)=0tx1etdtandx>0(gammaeulerfunction)provethatΓ(x)=limn>∝(n!)nxn(n+1)(n+2)...(n+x)

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