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IntegrationQuestion and Answers: Page 316

Question Number 26584 Answers: 0 Comments: 4

∫_a ^x (x−t)^5 y(t)dt=4x^6 y(x)=...

$\int_{a}^{x} {(x - t)}^{5} y (t) d t = 4 x^{6}$ $y (x) = . . .$

Question Number 26575 Answers: 0 Comments: 1

find the value of ∫_0 ^∞ e^(−[x]) sinxdx in that [x]=E(x)

$f i n d t h e v a l u e o f \int_{0}^{\infty} e^{- [x]} s i n x d x i n t h a t [x] = E (x)$

Question Number 26559 Answers: 0 Comments: 1

let put F(x)= ∫_0 ^∞ e^(−tx) ((sint)/t) dt with x≥0 we accept that F is class C^1 on [0,∝[ calculate (∂F/∂x) and find F(x) then find the value of ∫_0 ^∞ ((sint)/t) dt

$l e t p u t F (x) = \int_{0}^{\infty} e^{- t x} \frac{s i n t}{t} d t w i t h x ⩾ 0$ $w e a c c e p t t h a t F i s c l a s s C^{1} o n [0, \propto [$ $c a l c u l a t e \frac{\partial F}{\partial x} a n d f i n d F (x)$ $t h e n f i n d t h e v a l u e o f \int_{0}^{\infty} \frac{s i n t}{t} d t$

Question Number 26558 Answers: 0 Comments: 1

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

$f i n d t h e v a l u e o f \int_{0}^{\infty} \frac{s i n x}{x (1 + x^{2})} d x$

Question Number 26507 Answers: 1 Comments: 0

∫_0 ^Π ((xsinx)/(1+cos^2 x))dx

${\int^{Π}}_{0} \frac{xsinx}{1 + \cos^{2} x} dx$

Question Number 26486 Answers: 1 Comments: 5

∫_( −1) ^( 1) ((xdx)/((x^2 + 1)^2 ))

$\int_{- 1}^{1} \frac{xdx}{{(x^{2} + 1)}^{2}}$

Question Number 26495 Answers: 0 Comments: 0

Question Number 26463 Answers: 0 Comments: 1

∫_0 ^(2π) cos^2 θsin θdθ

$\int_{0}^{2 π} \cos^{2} θ \sin θ d θ$

Question Number 26452 Answers: 1 Comments: 0

∫(√(tanx))

$\int \sqrt{t a n x}$

Question Number 26446 Answers: 1 Comments: 0

Question Number 26403 Answers: 0 Comments: 5

developp the function f(x)=/x/ 2π periodic in fourier serie .(f even)

$d e v e l o p p t h e f u n c t i o n f (x) = / x / 2 π$ $p e r i o d i c i n f o u r i e r s e r i e . (f e v e n)$

Question Number 26399 Answers: 2 Comments: 0

calculate ∫∫ _D cos(x^2 +y^2 )dxdy with D=C(o.(√(π/2))).

$c a l c u l a t e \int \int_{D} c o s (x^{2} + y^{2}) d x d y w i t h D = C (o . \sqrt{\frac{π}{2}}) .$

Question Number 26398 Answers: 2 Comments: 2

find the value of ∫∫_D x^2 y dxdy on the domain D={(x.y)∈R^2 / x^2 +y^2 −2x≤0 and y≥0}

$f i n d t h e v a l u e o f \int \int_{D} x^{2} y d x d y o n t h e d o m a i n$ $D = {(x . y) \in R^{2} / x^{2} + y^{2} - 2 x ⩽ 0 a n d y ⩾ 0}$

Question Number 26397 Answers: 2 Comments: 1

find ∫ (dx/(x(√(1+x^2 )))) and calculate ∫_1 ^3 (dx/(x(√(1+x^2 ))))

$f i n d \int \frac{d x}{x \sqrt{1 + x^{2}}} a n d c a l c u l a t e \int_{1}^{3} \frac{d x}{x \sqrt{1 + x^{2}}}$

Question Number 26396 Answers: 1 Comments: 1

find the value of ∫_0 ^(1 ) (dx/(x^2 +2x +5)) .

$f i n d t h e v a l u e o f \int_{0}^{1} \frac{d x}{x^{2} + 2 x + 5} .$

Question Number 26395 Answers: 1 Comments: 0

find ∫ (dx/(x(√(x^2 +x−1))))

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

Question Number 26362 Answers: 0 Comments: 0

find the value of ∫_0 ^∝ e^(−x) lnx dx for that use A_n = ∫_0 ^n (1− (t/n))^(n−1) ln(t) dt .

$f i n d t h e v a l u e o f \int_{0}^{\propto} e^{- x} l n x d x f o r t h a t u s e$ $A_{n} = \int_{0}^{n} {(1 - \frac{t}{n})}^{n - 1} l n (t) d t .$

Question Number 26360 Answers: 0 Comments: 1

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

$f i n d t h e v a l u e o f \int_{0}^{\propto} \frac{c o s (α x)}{1 + x^{2}} d x .$

Question Number 26359 Answers: 0 Comments: 2

find lim_(n−>∝) ∫_0 ^n (1−(t/n))^(n−1) dt .

$f i n d {l i m}_{n - >\propto} \int_{0}^{n} {(1 - \frac{t}{n})}^{n - 1} d t .$

Question Number 26358 Answers: 1 Comments: 0

find the value of ∫_0 ^(π/4) tan^n x dx with n element from N.

$f i n d t h e v a l u e o f \int_{0}^{\frac{π}{4}} {t a n}^{n} x d x w i t h$ $n e l e m e n t f r o m N .$

Question Number 26357 Answers: 1 Comments: 1

find the value of ∫_0 ^(π/2) ln(cosθ)dθ and ∫_0 ^(π/2) ln(sinθ)dθ .

$f i n d t h e v a l u e o f \int_{0}^{\frac{π}{2}} l n (c o s θ) d θ a n d$ $\int_{0}^{\frac{π}{2}} l n (s i n θ) d θ .$

Question Number 26270 Answers: 0 Comments: 1

∫(√(cosec(x)))dx

$\int \sqrt{c o s e c (x)} d x$

Question Number 26248 Answers: 0 Comments: 0

lim_(n→∞) ∫_0 ^1 (x^n /(cos x))dx=

$\lim_{n \to \infty} \int_{0}^{1} \frac{x^{n}}{\cos x} d x =$

Question Number 26242 Answers: 0 Comments: 1

prove that Σ_(k=0) ^(k=n) cos^2 (kx)= ((n+1)/2) + ((sin((n+1)x)cos(nx))/(2 sinx)) x from R−{ kπ.kεZ}then find the value of integral ∫_0 ^π ((sin((n+1)x)cos(nx))/(sinx))dx

$p r o v e t h a t \sum_{k = 0}^{k = n} {c o s}^{2} (k x) = \frac{n + 1}{2} + \frac{s i n ((n + 1) x) c o s (n x)}{2 s i n x}$ $x f r o m R - {k π . k ε Z} t h e n f i n d t h e v a l u e o f i n t e g r a l$ $\int_{0}^{π} \frac{s i n ((n + 1) x) c o s (n x)}{s i n x} d x$

Question Number 26241 Answers: 0 Comments: 2

∫(√(sin θ))dθ integration ?? solve quickly

$\int \sqrt{\sin θ} d θ$ $i n t e g r a t i o n ? ?$ $s o l v e q u i c k l y$

Question Number 26142 Answers: 0 Comments: 0

Prove that If f(x) is Riemann integrable on [a,b] and ∃M>0 s.t. ∀x∈[a,b] (f(x)≠0 and ∣f(x)∣<M and ∣(1/(f(x)))∣<M), then (1/(f(x))) is Riemann integrable on [a,b].

$Prove that$ $If f (x) is Riemann integrable on [a, b] and$ $\exists M > 0 s . t . \forall x \in [a, b] (f (x) \neq 0 a n d ∣ f (x) ∣< M a n d ∣ \frac{1}{f (x)} ∣< M),$ $then \frac{1}{f (x)} is Riemann integrable on [a, b] .$

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