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IntegrationQuestion and Answers: Page 114

Question Number 126179 Answers: 1 Comments: 0

let f(x)= e^(−2x) actan (3x+1) 1)calculste f^((n)) (x) and f^((n)) (0) 2) if f(x)=Σ a_n x^n determine the sequence a_n 3) calculate ∫_0 ^∞ f(x)dx

$let f (x) = e^{- 2 x} actan (3 x + 1)$ $1) calculste f^{(n)} (x) and f^{(n)} (0)$ $2) if f (x) = Σ a_{n} x^{n} determine the sequence a_{n}$ $3) calculate \int_{0}^{\infty} f (x) dx$

Question Number 126139 Answers: 1 Comments: 4

closed formula .... ∫_0 ^( 1) ((x^n ln(x))/(1+x))dx =?

$c l o s e d f o r m u l a . . . .$ $\int_{0}^{1} \frac{x^{n} l n (x)}{1 + x} d x = ?$

Question Number 126133 Answers: 2 Comments: 0

Question Number 126073 Answers: 0 Comments: 2

Question Number 126068 Answers: 1 Comments: 0

Question Number 126065 Answers: 1 Comments: 0

Show that:: Ω = ∫_0 ^( 1) ((Li_2 (x)log(x))/(1+x))dx = −(3/(16))ζ(4) Goodluck

$Show that ::$ $Ω = \int_{0}^{1} \frac{{Li}_{2} (x) \log (x)}{1 + x} dx = - \frac{3}{16} ζ (4)$ $Goodluck$

Question Number 126000 Answers: 3 Comments: 0

∫ (dx/((x−1)(√(x^2 −2x)))) ?

$\int \frac{d x}{(x - 1) \sqrt{x^{2} - 2 x}} ?$

Question Number 125999 Answers: 2 Comments: 1

Question Number 125997 Answers: 1 Comments: 0

Find the Riemann sum for the given function with the specified number of intervals using left endpoints f(x)= 4ln x+2x ; 1≤x≤4 n=7 . Round your answer to two decimal places ?

$F i n d t h e R i e m a n n s u m f o r t h e$ $g i v e n f u n c t i o n w i t h t h e s p e c i f i e d$ $n u m b e r o f i n t e r v a l s u s i n g l e f t$ $e n d p o i n t s f (x) = 4 \ln x + 2 x; 1 ⩽ x ⩽ 4$ $n = 7 . R o u n d y o u r a n s w e r t o t w o$ $d e c i m a l p l a c e s ?$

Question Number 125986 Answers: 1 Comments: 0

Question Number 125965 Answers: 1 Comments: 0

∫ cot x ln (sin x) dx ?

$\int \cot x \ln (\sin x) d x ?$

Question Number 125962 Answers: 1 Comments: 0

∫_1 ^3 x^(2x) (1+ln x) dx =?

$\underset{1}{\int^{3}} x^{2 x} (1 + \ln x) d x = ?$

Question Number 125949 Answers: 1 Comments: 0

Question Number 125922 Answers: 1 Comments: 0

...advanced calculus... evaluate ::: Ω=^(???) ∫_0 ^( ∞) cos(x^2 )ln(x)dx :::::::::

$. . . a d v a n c e d c a l c u l u s . . .$ $e v a l u a t e ::: Ω \overset{? ? ?}{=} \int_{0}^{\infty} c o s (x^{2}) l n (x) d x$ $:::::::::$

Question Number 125919 Answers: 0 Comments: 0

∫_0 ^∞ ∫_0 ^∞ ∫_0 ^∞ ∫_0 ^∞ ((dx dy dz dt)/((cosh(x)+cosh(y)+cosh(z)+cosh(t))^4 )) =((7ζ(3)−6)/(12))

$\int_{0}^{\infty} \int_{0}^{\infty} \int_{0}^{\infty} \int_{0}^{\infty} \frac{d x d y d z d t}{{(c o s h (x) + c o s h (y) + c o s h (z) + c o s h (t))}^{4}}$ $= \frac{7 ζ (3) - 6}{12}$

Question Number 125911 Answers: 1 Comments: 0

∫_0 ^( ∞) ((xln(1+x))/(1+x^4 ))dx

$\int_{0}^{\infty} \frac{xln (1 + x)}{1 + x^{4}} dx$

Question Number 125897 Answers: 0 Comments: 2

∫ (dx/(2+x+(√(1−x^2 )))) ?

$\int \frac{d x}{2 + x + \sqrt{1 - x^{2}}} ?$

Question Number 125895 Answers: 1 Comments: 0

∫ (dx/(tan^4 x+1)) ?

$\int \frac{d x}{\tan^{4} x + 1} ?$

Question Number 125893 Answers: 0 Comments: 0

∫ ((sin x cos x)/((1+(√(sin 2x)))^3 )) dx

$\int \frac{\sin x \cos x}{{(1 + \sqrt{\sin 2 x})}^{3}} d x$

Question Number 125889 Answers: 2 Comments: 0

∫ ((tan^3 x)/( (√(sec x)))) dx ?

$\int \frac{\tan^{3} x}{\sqrt{\sec x}} d x ?$

Question Number 125876 Answers: 0 Comments: 1

Question Number 125858 Answers: 0 Comments: 4

Question Number 125841 Answers: 1 Comments: 3

Given f(x)=f(x+2) ∀x∈R if ∫_0 ^2 f(x)dx=k then ∫_0 ^(1010) f(x+2a)dx ? for a∈Z

$G i v e n f (x) = f (x + 2) \forall x \in R$ $i f \underset{0}{\int^{2}} f (x) d x = k t h e n \underset{0}{\int^{1010}} f (x + 2 a) d x ?$ $f o r a \in Z$

Question Number 125711 Answers: 3 Comments: 0

I=∫((cos 2x)/(1+cos^2 x))dx =? please help

$I = \int \frac{\cos 2 x}{1 + \cos^{2} x} dx = ? please help$

Question Number 125684 Answers: 1 Comments: 0

.... INTEGRAL... prove that : ∫_0 ^( ∞) x^3 {ln(1+e^x ) −x}dx=((45)/8) ζ( 5 )

$. . . . INTEGRAL . . .$ $prove that :$ $\int_{0}^{\infty} x^{3} {l n (1 + e^{x}) - x} d x = \frac{45}{8} ζ (5)$

Question Number 125542 Answers: 1 Comments: 1

∫x^7 (√(1−x^3 ))dx=?

$\int x^{7} \sqrt{1 - x^{3}} d x = ?$

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