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IntegrationQuestion and Answers: Page 279

Question Number 38113 Answers: 0 Comments: 2

let p>1 calculate ∫_0 ^(2π) (dt/((p +cost)^2 ))

$l e t p > 1 c a l c u l a t e \int_{0}^{2 π} \frac{d t}{{(p + c o s t)}^{2}}$

Question Number 38111 Answers: 1 Comments: 1

find lim_(x→0) ((e^x −[x])/x)

$f i n d {l i m}_{x \to 0} \frac{e^{x} - [x]}{x}$

Question Number 38110 Answers: 0 Comments: 0

let x from R find the value of f(x)= ∫_0 ^π ln(x^2 −2x cosθ +1)dθ

$l e t x f r o m R f i n d t h e v a l u e o f$ $f (x) = \int_{0}^{π} l n (x^{2} - 2 x c o s θ + 1) d θ$

Question Number 38107 Answers: 0 Comments: 0

find C = Σ_(n=1) ^∞ ((cos(nx))/n^2 )dx and S=Σ_(n=1) ^∞ ((sin(nx))/n^2 )

$f i n d C = \sum_{n = 1}^{\infty} \frac{c o s (n x)}{n^{2}} d x a n d S = \sum_{n = 1}^{\infty} \frac{s i n (n x)}{n^{2}}$

Question Number 38106 Answers: 0 Comments: 1

calculate ∫_0 ^(+∞) e^(−3t) ln(1+e^t )dt .

$c a l c u l a t e \int_{0}^{+ \infty} e^{- 3 t} l n (1 + e^{t}) d t .$

Question Number 38105 Answers: 1 Comments: 0

find ∫ (dx/((√(2x+1)) +(√(2x−1))))

$f i n d \int \frac{d x}{\sqrt{2 x + 1} + \sqrt{2 x - 1}}$

Question Number 38104 Answers: 1 Comments: 0

find ∫_1 ^(+∞) (dx/((x^2 +2)(√(x+3))))

$f i n d \int_{1}^{+ \infty} \frac{d x}{(x^{2} + 2) \sqrt{x + 3}}$

Question Number 38103 Answers: 0 Comments: 0

find I(λ)= ∫_0 ^(π/2) ((xdx)/(λ +tanx)) λ from R.

$f i n d I (λ) = \int_{0}^{\frac{π}{2}} \frac{x d x}{λ + t a n x} λ f r o m R .$

Question Number 38102 Answers: 0 Comments: 0

let B_n = ∫_0 ^n e^(−(x−[x])^2 ) dx 1) calculate B_n 2) find lim_(n→+∞) B_n

$l e t B_{n} = \int_{0}^{n} e^{- {(x - [x])}^{2}} d x$ $1) c a l c u l a t e B_{n}$ $2) f i n d {l i m}_{n \to + \infty} B_{n}$

Question Number 38101 Answers: 0 Comments: 1

let A_n = ∫_0 ^n e^(x−[x]) dx 1) calculate A_n 2) find lim_(n→+∞) A_n

$l e t A_{n} = \int_{0}^{n} e^{x - [x]} d x$ $1) c a l c u l a t e A_{n}$ $2) f i n d {l i m}_{n \to + \infty} A_{n}$

Question Number 38100 Answers: 0 Comments: 1

let A_n = ∫_0 ^n (x−[x])^2 dx 1) calculate A_n 2) find lim_(n→+∞) A_n

$l e t A_{n} = \int_{0}^{n} {(x - [x])}^{2} d x$ $1) c a l c u l a t e A_{n}$ $2) f i n d {l i m}_{n \to + \infty} A_{n}$

Question Number 38074 Answers: 1 Comments: 4

∫(dx/(a+btan^2 x)) = ?

$\int \frac{d x}{a + b \tan^{2} x} = ?$

Question Number 38058 Answers: 3 Comments: 0

∫((tan x)/(a+btan^2 x)) dx = ?

$\int \frac{\tan x}{a + b \tan^{2} x} d x = ?$

Question Number 38057 Answers: 1 Comments: 0

∫((cos 5x+cos 4x)/(1−2cos 3x))dx = ?

$\int \frac{\cos 5 x + \cos 4 x}{1 - 2 \cos 3 x} d x = ?$

Question Number 37961 Answers: 1 Comments: 0

calculate ∫_0 ^∞ (dx/(x^(2 ) +(√(1+x^2 )))) .

$c a l c u l a t e \int_{0}^{\infty} \frac{d x}{x^{2} + \sqrt{1 + x^{2}}} .$

Question Number 37938 Answers: 5 Comments: 5

Question Number 37922 Answers: 1 Comments: 2

f : N → R g : N → R f(n)=∫_0 ^(2π) x^n sin x dx g(n)=∫_0 ^(2π) x^n cos x dx ((f(n+1)−f(n))/(g(n+1)−g(n)))=?

$f : N \to R$ $g : N \to R$ $f (n) = \int_{0}^{2 π} x^{n} \sin x d x$ $g (n) = \int_{0}^{2 π} x^{n} \cos x d x$ $\frac{f (n + 1) - f (n)}{g (n + 1) - g (n)} = ?$

Question Number 37912 Answers: 1 Comments: 1

Evaluate : the Integral ∫_(-(π/2)) ^(π/2) ∫_0 ^(3 cos θ) r^2 sin^2 θ. dr dθ

$Evaluate : the Integral$ $\int_{- \frac{π}{2}}^{\frac{π}{2}} \int_{0}^{3 \cos θ} r^{2} \sin^{2} θ . d r d θ$

Question Number 37902 Answers: 2 Comments: 1

ind the value of f(a) =∫_0 ^(+∞) (dx/(x^2 +(√(a^2 +x^2 )))) dx witha>0 2)calculate f^′ (a) .

$i n d t h e v a l u e o f f (a) = \int_{0}^{+ \infty} \frac{d x}{x^{2} + \sqrt{a^{2} + x^{2}}} d x$ $w i t h a > 0$ $2) c a l c u l a t e f^{^{'}} (a) .$

Question Number 37898 Answers: 1 Comments: 1

calculate f(λ) = ∫_0 ^(+∞) e^(−λx) cos(π[x])dx withλ>0

$c a l c u l a t e f (λ) = \int_{0}^{+ \infty} e^{- λ x} c o s (π [x]) d x$ $w i t h λ > 0$

Question Number 37896 Answers: 2 Comments: 1

let I_n = ∫_0 ^n (((−1)^([x]) )/((2x+1)^2 ))dx 1) calculate I_n interms of n 2) find lim_(n→+∞) I_n

$l e t I_{n} = \int_{0}^{n} \frac{{(- 1)}^{[x]}}{{(2 x + 1)}^{2}} d x$ $1) c a l c u l a t e I_{n} i n t e r m s o f n$ $2) f i n d {l i m}_{n \to + \infty} I_{n}$

Question Number 37895 Answers: 1 Comments: 0

calculate A_n =∫_0 ^n (x−[(√x)])dx and lim_(n→+∞) A_n

$c a l c u l a t e A_{n} = \int_{0}^{n} (x - [\sqrt{x}]) d x a n d$ ${l i m}_{n \to + \infty} A_{n}$

Question Number 37893 Answers: 1 Comments: 1

calculate ∫_0 ^1 (√(x+(√(x+1)))) dx .

$c a l c u l a t e \int_{0}^{1} \sqrt{x + \sqrt{x + 1}} d x .$

Question Number 37889 Answers: 0 Comments: 0

calculate ∫_0 ^∞ ((arctan(2x))/x) e^(−tx) dx with t ≥0

$c a l c u l a t e \int_{0}^{\infty} \frac{a r c t a n (2 x)}{x} e^{- t x} d x w i t h t ⩾ 0$

Question Number 37888 Answers: 1 Comments: 2

find f(α) = ∫_0 ^1 arctan(e^(−αx) )dx with α≥0

$f i n d f (α) = \int_{0}^{1} a r c t a n (e^{- α x}) d x w i t h α ⩾ 0$

Question Number 37887 Answers: 0 Comments: 0

find f(α) = ∫_0 ^1 arctan(1+e^(−αx) )dx with α≥0

$f i n d f (α) = \int_{0}^{1} a r c t a n (1 + e^{- α x}) d x w i t h α ⩾ 0$

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