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IntegrationQuestion and Answers: Page 303 |
calculate ∫_0 ^(π/4) (dt/((1+sin^2 t)^2 )) . |
calculate ∫_0 ^(π/4) cos(x)ln(cos(x))dx . |
find the value of ∫_0 ^1 arctan((√(1−x^2 )))dx |
calculate ∫_0 ^(π/2) (dt/(1+cosθ sint)) . |
calculate ∫_0 ^1 ^3 (√(x^2 (1−x))) dx |
find the value of ∫_0 ^π ((xdx)/(1+sinx)) . |
calculate ∫_0 ^(2π) (dt/(x−e^(it) )) . |
find the value of ∫∫_D ((dxdy)/((4x^2 +y^2 +1)^2 )) D={(x,y)∈ R^2 / x^2 +y^2 ≤1 and y ≤2x } . |
let give λ from R and λ^2 ≠1 and I_n (λ) = ∫_0 ^π ((cos(nt))/(1−2λcost +λ^2 ))dt .calculate I_n (λ). |
find the value of ∫_0 ^∞ ((sin^3 t)/t^2 ) dt . |
calculate ∫_0 ^(+∞) ((th(3x) −th(2x))/x) dx . |
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. |
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