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IntegrationQuestion and Answers: Page 300 |
find the value of ∫_0 ^1 ((ln(t))/((1+t)(√(1−t^2 )))) dt. |
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)))) . |
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) |
find lim_(x→+∞) e^(−x^2 ) ∫_0 ^x e^t^2 dt . |
calculate ∫_1 ^2 (dx/(x +x(√x))) . |
calculate ∫_1 ^e ln(1+(√x))dx . |
find ∫ (x^3 /(√(1+x^2 ))) dx |
find ∫ (1/(2−x^2 )) dx |
Find Σ_(k=1) ^∞ (∫_(k−1) ^k x^(−x) dx) . |
Find the ∫ ((x+1)/(x^2 +x+1))dx |
find lim_(n→∞) ∫_0 ^∞ e^(−t) sin^n t dt . |
fimd lim_(x→0) (1/x^3 ) ∫_0 ^x t^2 ln(1+sint) dt . |
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) . |
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 . |
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. |
let u_n = ∫_0 ^1 (dx/(1+x+...+x^n )) study the convergence of Σ u_n . |
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 . |
calculate ∫_0 ^∞ e^(−αx) ln(x) dx with α>0 . |
let α>0 prove that Σ_(n=0) ^∞ (((−1)^n )/(n+α)) =∫_0 ^1 (x^(α−1) /(1+x))dx . |
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)) |
find the nature of ∫_2 ^∞ (e^(−x) /(√(x^2 −4))) dx . |
find the value of ∫_0 ^∞ (((1+t^2 )/(1+t^4 )))arctant dt. |
find ∫_2 ^(√5) x(√((x−2)((√5)−x))) dx . |
find the value of ∫_0 ^∞ ((arctanx)/(x^2 +x+1))dx . |
Evaluate ∫sin (√x)dx |
∫((sinx)/x)dx |
Pg 295 Pg 296 Pg 297 Pg 298 Pg 299 Pg 300 Pg 301 Pg 302 Pg 303 Pg 304 |