Question and Answers Forum

IntegrationQuestion and Answers: Page 222

Question Number 65015 Answers: 1 Comments: 3

∫(((√(x+1)) − (√(x−1)))/((√(x+1)) + (√(x−1)))) dx

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

Question Number 65004 Answers: 0 Comments: 1

let U_n = ∫_(1/n) ^(2/n) Γ(x)Γ(1−x)dx with n≥3 1) calculate and determine lim_(n→+∞) U_n 2) study the convergence of Σ U_n

$l e t U_{n} = \int_{\frac{1}{n}}^{\frac{2}{n}} Γ (x) Γ (1 - x) d x w i t h n ⩾ 3$ $1) c a l c u l a t e a n d d e t e r m i n e {l i m}_{n \to + \infty} U_{n}$ $2) s t u d y t h e c o n v e r g e n c e o f Σ U_{n}$

Question Number 65003 Answers: 0 Comments: 0

find ∫_0 ^∞ (dx/(Γ(x))) with Γ(x) =∫_0 ^∞ t^(x−1) e^(−t) dt (x>0)

$f i n d \int_{0}^{\infty} \frac{d x}{Γ (x)} w i t h Γ (x) = \int_{0}^{\infty} t^{x - 1} e^{- t} d t (x > 0)$

Question Number 64994 Answers: 1 Comments: 1

∫(√(tanh(x))) dx

$\int \sqrt{t a n h (x)} d x$

Question Number 64993 Answers: 0 Comments: 0

let f(a) =∫_0 ^∞ ((cos(x^2 )−sin(x^2 ))/((x^2 +a^2 )^2 ))dx with a>0 1) calculate f(a) 2) find the values of ∫_0 ^∞ ((cos(x^2 )−sin(x^2 ))/((x^2 +1)^2 )) and ∫_0 ^∞ ((cos(x^2 )−sin(x^2 ))/((x^2 +3)^2 ))dx .

$l e t f (a) = \int_{0}^{\infty} \frac{c o s (x^{2}) - s i n (x^{2})}{{(x^{2} + a^{2})}^{2}} d x w i t h a > 0$ $1) c a l c u l a t e f (a)$ $2) f i n d t h e v a l u e s o f \int_{0}^{\infty} \frac{c o s (x^{2}) - s i n (x^{2})}{{(x^{2} + 1)}^{2}} a n d$ $\int_{0}^{\infty} \frac{c o s (x^{2}) - s i n (x^{2})}{{(x^{2} + 3)}^{2}} d x .$

Question Number 64975 Answers: 0 Comments: 1

Question Number 64970 Answers: 0 Comments: 9

let f(a)=∫_0 ^∞ ((cos(x^2 ) +sin(x^2 ))/((x^2 +a^2 )^2 )) dx with a>0 1) calculate f(a) 2) find the values of ∫_0 ^∞ ((cos(x^2 )+sin(x^2 ))/((x^2 +1)^2 ))dx and ∫_0 ^∞ ((cos(x^2 )+sin(x^2 ))/((x^2 +3)^2 ))dx

$l e t f (a) = \int_{0}^{\infty} \frac{c o s (x^{2}) + s i n (x^{2})}{{(x^{2} + a^{2})}^{2}} d x w i t h a > 0$ $1) c a l c u l a t e f (a)$ $2) f i n d t h e v a l u e s o f \int_{0}^{\infty} \frac{c o s (x^{2}) + s i n (x^{2})}{{(x^{2} + 1)}^{2}} d x a n d$ $\int_{0}^{\infty} \frac{c o s (x^{2}) + s i n (x^{2})}{{(x^{2} + 3)}^{2}} d x$

Question Number 64905 Answers: 0 Comments: 0

∫log (tan x)dx

$\int \log (\tan x) dx$

Question Number 64904 Answers: 0 Comments: 2

calculate ∫_1 ^2 ∫_0 ^x (1/((x^2 +y^2 )^(3/2) ))dydx

$c a l c u l a t e \int_{1}^{2} \int_{0}^{x} \frac{1}{{(x^{2} + y^{2})}^{\frac{3}{2}}} d y d x$

Question Number 64866 Answers: 0 Comments: 3

find ∫_1 ^(+∞) (dx/(x^2 (√(1+x+x^2 ))))

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

Question Number 64850 Answers: 0 Comments: 4

let A_λ =∫_0 ^π (dx/(λ +cosx +sinx)) (λ ∈ R) 1) find a explicit form of A_λ 2) find also B_λ =∫_0 ^π (dx/((λ +cosx +sinx)^2 )) 3) calculate ∫_0 ^π (dx/(2+cosx +sinx)) and ∫_0 ^π (dx/((3+cosx +sinx)^2 ))

$l e t A_{λ} = \int_{0}^{π} \frac{d x}{λ + c o s x + s i n x} (λ \in R)$ $1) f i n d a e x p l i c i t f o r m o f A_{λ}$ $2) f i n d a l s o B_{λ} = \int_{0}^{π} \frac{d x}{{(λ + c o s x + s i n x)}^{2}}$ $3) c a l c u l a t e \int_{0}^{π} \frac{d x}{2 + c o s x + s i n x} a n d \int_{0}^{π} \frac{d x}{{(3 + c o s x + s i n x)}^{2}}$

Question Number 64818 Answers: 2 Comments: 1

find ∫ (dx/(1+cosx +cos(2x)))

$f i n d \int \frac{d x}{1 + c o s x + c o s (2 x)}$

Question Number 64805 Answers: 0 Comments: 0

∫log(((1+sinhx))/((1−sinhx)))tanhx dx

$\int l o g \frac{(1 + s i n h x)}{(1 - s i n h x)} t a n h x d x$

Question Number 64802 Answers: 1 Comments: 1

∫(cos^4 x+sin^4 x)/(cos2x+1)dx

$\int ({c o s}^{4} x + {s i n}^{4} x) / (c o s 2 x + 1) d x$

Question Number 64801 Answers: 0 Comments: 0

∫(cos^4 x+sin^4 x)/(cos2x+1)dx

$\int ({c o s}^{4} x + {s i n}^{4} x) / (c o s 2 x + 1) d x$

Question Number 64762 Answers: 1 Comments: 1

Given that g(x)=(2/((1+x)(1+3x^2 )) a) express g(x) in partial fractions. b) evaluate ∫_0 ^1 g((x) dx.

$Given that g (x) = \frac{2}{(1 + x) (1 + {3 x}^{2}}$ $a) express g (x) in partial fractions .$ $b) evaluate \int_{0}^{1} g ((x) dx .$

Question Number 64759 Answers: 0 Comments: 0

∫((ln(ln(x)))/((ln(x))^n )) dx , n≠1

$\int \frac{l n (l n (x))}{{(l n (x))}^{n}} d x, n \neq 1$

Question Number 64745 Answers: 0 Comments: 1

calculate ∫_0 ^1 ((sin(lnx))/(lnx))dx

$c a l c u l a t e \int_{0}^{1} \frac{s i n (l n x)}{l n x} d x$

Question Number 64873 Answers: 0 Comments: 4

let f(x) =∫_0 ^π (dt/(x+sint)) with xreal 1) find a explicit form of f(x) 2) find also g(x) =∫_0 ^π (dt/((x+sint)^2 )) 3) give f^((n)) (x) at form of integral 4) calculate ∫_0 ^π (dt/(3+sint)) and ∫_0 ^π (dt/((3+sint)^2 ))

$l e t f (x) = \int_{0}^{π} \frac{d t}{x + s i n t} w i t h x r e a l$ $1) f i n d a e x p l i c i t f o r m o f f (x)$ $2) f i n d a l s o g (x) = \int_{0}^{π} \frac{d t}{{(x + s i n t)}^{2}}$ $3) g i v e f^{(n)} (x) a t f o r m o f i n t e g r a l$ $4) c a l c u l a t e \int_{0}^{π} \frac{d t}{3 + s i n t} a n d \int_{0}^{π} \frac{d t}{{(3 + s i n t)}^{2}}$

Question Number 64735 Answers: 0 Comments: 2

∫tanθ/1+^− sinθ dθ

$\int t a n θ / 1 \bar{+} s i n θ d θ$

Question Number 64733 Answers: 0 Comments: 0

∫(secθtanθ)dθ/secθ+^− tanθ

$\int (s e c θ t a n θ) d θ / s e c θ \bar{+} t a n θ$

Question Number 64687 Answers: 0 Comments: 1

Question Number 64677 Answers: 0 Comments: 4

let f(x) =∫_0 ^1 lnt ln(1−xt)dt with ∣x∣<1 1)determine a explicit form for f(x) 2) find also g(x) =∫_0 ^1 ((tlnt)/(1−xt))dt 3) give f^((n)) (x) at form of integral 4) calculate ∫_0 ^1 ln(t)ln(1−t)dt and ∫_0 ^1 ln(t)ln(2−t)dt 5) calculate ∫_0 ^1 ((tln(t))/(2−t)) dt .

$l e t f (x) = \int_{0}^{1} l n t l n (1 - x t) d t w i t h ∣ x ∣< 1$ $1) d e t e r m i n e a e x p l i c i t f o r m f o r f (x)$ $2) f i n d a l s o g (x) = \int_{0}^{1} \frac{t l n t}{1 - x t} d t$ $3) g i v e f^{(n)} (x) a t f o r m o f i n t e g r a l$ $4) c a l c u l a t e \int_{0}^{1} l n (t) l n (1 - t) d t a n d \int_{0}^{1} l n (t) l n (2 - t) d t$ $5) c a l c u l a t e \int_{0}^{1} \frac{t l n (t)}{2 - t} d t .$

Question Number 64662 Answers: 1 Comments: 3

∫(dx/((x^8 +x^4 +1)^2 )) ∫_(1/x) ^x ((ln(t))/(t^2 +1)) dt

$\int \frac{d x}{{(x^{8} + x^{4} + 1)}^{2}}$ $\int_{\frac{1}{x}}^{x} \frac{l n (t)}{t^{2} + 1} d t$

Question Number 64649 Answers: 1 Comments: 1

calculate ∫_0 ^(2π) ((cosθ)/(5+3cosθ))dθ

$c a l c u l a t e \int_{0}^{2 π} \frac{c o s θ}{5 + 3 c o s θ} d θ$

Question Number 64642 Answers: 0 Comments: 1

∫(dx)/e^x +x

$\int (d x) / e^{x} + x$

Pg 217 Pg 218 Pg 219 Pg 220 Pg 221 Pg 222 Pg 223 Pg 224 Pg 225 Pg 226

Contact: info@tinkutara.com