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IntegrationQuestion and Answers: Page 300

Question Number 32338    Answers: 0   Comments: 0

find the value of ∫_0 ^1 ((ln(t))/((1+t)(√(1−t^2 )))) dt.

findthevalueof01ln(t)(1+t)1t2dt.

Question Number 32337    Answers: 0   Comments: 0

1)calculate ∫_a ^(+∞) (dx/((1+x^2 )(√(x^2 −a^2 )))) with a>0 2) find the value of ∫_2 ^(+∞) (dx/((1+x^2 )(√(x^2 −4)))) .

1)calculatea+dx(1+x2)x2a2witha>02)findthevalueof2+dx(1+x2)x24.

Question Number 32323    Answers: 1   Comments: 0

Given f(x) = (3/(16))(∫_0 ^1 f(x)dx)x^2 − (9/(10))(∫_0 ^2 f(x)dx)x + 2(∫_0 ^3 f(x)dx) + 4 Find f(x)

Givenf(x)=316(01f(x)dx)x2910(02f(x)dx)x+2(03f(x)dx)+4Findf(x)

Question Number 32304    Answers: 0   Comments: 0

find lim_(x→+∞) e^(−x^2 ) ∫_0 ^x e^t^2 dt .

findlimx+ex20xet2dt.

Question Number 32302    Answers: 1   Comments: 0

calculate ∫_1 ^2 (dx/(x +x(√x))) .

calculate12dxx+xx.

Question Number 32301    Answers: 0   Comments: 1

calculate ∫_1 ^e ln(1+(√x))dx .

calculate1eln(1+x)dx.

Question Number 32269    Answers: 1   Comments: 0

find ∫ (x^3 /(√(1+x^2 ))) dx

findx31+x2dx

Question Number 32258    Answers: 2   Comments: 0

find ∫ (1/(2−x^2 )) dx

find12x2dx

Question Number 32206    Answers: 0   Comments: 0

Find Σ_(k=1) ^∞ (∫_(k−1) ^k x^(−x) dx) .

Findk=1(kk1xxdx).

Question Number 32139    Answers: 0   Comments: 4

Find the ∫ ((x+1)/(x^2 +x+1))dx

Findthex+1x2+x+1dx

Question Number 32045    Answers: 0   Comments: 0

find lim_(n→∞) ∫_0 ^∞ e^(−t) sin^n t dt .

findlimn0etsinntdt.

Question Number 32044    Answers: 0   Comments: 1

fimd lim_(x→0) (1/x^3 ) ∫_0 ^x t^2 ln(1+sint) dt .

fimdlimx01x30xt2ln(1+sint)dt.

Question Number 32043    Answers: 0   Comments: 0

let f(x)= ∫_x ^x^2 (dt/(lnt)) with x>0 and x≠1 1) prove that ∀ x>1 ∫_x ^x^2 ((xdt)/(tlnt)) ≤f(x)≤ ∫_x ^x^2 ((x^2 dt)/(tlnt)) after find lim_(x→1) f(x) 2) calculate f^′ (x) .

letf(x)=xx2dtlntwithx>0andx11)provethatx>1xx2xdttlntf(x)xx2x2dttlntafterfindlimx1f(x)2)calculatef(x).

Question Number 32040    Answers: 0   Comments: 2

let give f(x) =∫_0 ^(π/2) (dt/(1+x tant)) 1) find a simple form of f(x) 2) calculate ∫_0 ^(π/2) ((tant)/((1+xtant)^2 ))dt 3)give the value of ∫_0 ^(π/2) ((tant)/((1+(√3) tant)^2 )) dt .

letgivef(x)=0π2dt1+xtant1)findasimpleformoff(x)2)calculate0π2tant(1+xtant)2dt3)givethevalueof0π2tant(1+3tant)2dt.

Question Number 32039    Answers: 0   Comments: 3

a>−1 calculate ∫_0 ^(π/2) (dt/(1+a tan^2 t)) . 2) find ∫_0 ^(π/2) ((tan^2 t)/((1+atan^2 t)^2 )) dt 3) find the value of ∫_0 ^(π/2) ((tan^2 t)/((1+2tan^2 t)^2 ))dt.

a>1calculate0π2dt1+atan2t.2)find0π2tan2t(1+atan2t)2dt3)findthevalueof0π2tan2t(1+2tan2t)2dt.

Question Number 32034    Answers: 0   Comments: 0

let u_n = ∫_0 ^1 (dx/(1+x+...+x^n )) study the convergence of Σ u_n .

letun=01dx1+x+...+xnstudytheconvergenceofΣun.

Question Number 32031    Answers: 0   Comments: 1

let f(a) = ∫_0 ^∞ e^(−ax) ln(x)dx with a>0 1) find f(a) 2) find ∫_0 ^∞ e^(−ax) (xlnx)dx 3) calculate ∫_0 ^∞ e^(−2x) (xlnx)dx .

letf(a)=0eaxln(x)dxwitha>01)findf(a)2)find0eax(xlnx)dx3)calculate0e2x(xlnx)dx.

Question Number 32029    Answers: 0   Comments: 0

calculate ∫_0 ^∞ e^(−αx) ln(x) dx with α>0 .

calculate0eαxln(x)dxwithα>0.

Question Number 32026    Answers: 0   Comments: 1

let α>0 prove that Σ_(n=0) ^∞ (((−1)^n )/(n+α)) =∫_0 ^1 (x^(α−1) /(1+x))dx .

letα>0provethatn=0(1)nn+α=01xα11+xdx.

Question Number 31974    Answers: 0   Comments: 0

1)find I(p,q) = ∫_0 ^1 t^p (1−t)^q dt with pand q integrs 2) find the nature of Σ I_((n,n))

1)findI(p,q)=01tp(1t)qdtwithpandqintegrs2)findthenatureofΣI(n,n)

Question Number 31970    Answers: 0   Comments: 0

find the nature of ∫_2 ^∞ (e^(−x) /(√(x^2 −4))) dx .

findthenatureof2exx24dx.

Question Number 31969    Answers: 0   Comments: 1

find the value of ∫_0 ^∞ (((1+t^2 )/(1+t^4 )))arctant dt.

findthevalueof0(1+t21+t4)arctantdt.

Question Number 31968    Answers: 0   Comments: 0

find ∫_2 ^(√5) x(√((x−2)((√5)−x))) dx .

find25x(x2)(5x)dx.

Question Number 31967    Answers: 0   Comments: 1

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

findthevalueof0arctanxx2+x+1dx.

Question Number 31951    Answers: 1   Comments: 0

Evaluate ∫sin (√x)dx

Evaluatesinxdx

Question Number 31858    Answers: 0   Comments: 1

∫((sinx)/x)dx

sinxxdx

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