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IntegrationQuestion and Answers: Page 121

Question Number 122614 Answers: 4 Comments: 0

Question Number 122588 Answers: 2 Comments: 0

Find the arc length of the curve x=(1/4)y^2 −(1/2)ln (y) between the points with the ordinates y=1 and y=2.

$F i n d t h e arc l e n g t h o f t h e c u r v e$ $x = \frac{1}{4} y^{2} - \frac{1}{2} \ln (y) b e t w e e n t h e p o i n t s$ $w i t h t h e o r d i n a t e s y = 1 a n d y = 2 .$

Question Number 122587 Answers: 5 Comments: 0

∫_1 ^(16) arctan (√((√x) −1)) dx ∫_0 ^(π/2) sin (2x) arctan (sin x) dx

$\underset{1}{\int^{16}} \arctan \sqrt{\sqrt{x} - 1} d x$ $\underset{0}{\int^{π / 2}} \sin (2 x) \arctan (\sin x) d x$

Question Number 122572 Answers: 1 Comments: 0

Question Number 122544 Answers: 0 Comments: 0

any one can explain me about Fresnel integral ?

$a n y o n e c a n e x p l a i n m e a b o u t$ $F r e s n e l i n t e g r a l ?$

Question Number 122542 Answers: 1 Comments: 0

∫_0 ^3 (√(1+cos (x^2 ))) dx ?

$\underset{0}{\int^{3}} \sqrt{1 + \cos (x^{2})} d x ?$

Question Number 122528 Answers: 1 Comments: 0

...nice calculus... Ω =∫_0 ^( (π/2)) xsin(x).cos(x)ln(sin(x).ln(cos(x))dx =^(???) (π/(16))−(π^3 /(192)) ✓

$. . . n i c e c a l c u l u s . . .$ $Ω = \int_{0}^{\frac{π}{2}} x s i n (x) . c o s (x) l n (s i n (x) . l n (c o s (x)) d x$ $\overset{? ? ?}{=} \frac{π}{16} - \frac{π^{3}}{192} ✓$

Question Number 122506 Answers: 1 Comments: 0

Question Number 122496 Answers: 2 Comments: 0

V=∫_0 ^3 ((x dx)/( (√(x+1))+(√(5x+1)))) T=∫_(−π/2) ^(π/2) (√(cos x−cos^3 x)) dx

$V = \underset{0}{\int^{3}} \frac{x d x}{\sqrt{x + 1} + \sqrt{5 x + 1}}$ $T = \underset{- π / 2}{\int^{π / 2}} \sqrt{\cos x - \cos^{3} x} d x$

Question Number 122469 Answers: 1 Comments: 5

Question Number 122461 Answers: 2 Comments: 2

∫ (x/((x^2 +a^2 )(x^3 +b^2 ))) ?

$\int \frac{x}{(x^{2} + a^{2}) (x^{3} + b^{2})} ?$

Question Number 122432 Answers: 0 Comments: 0

Question Number 122430 Answers: 1 Comments: 0

∫ (x^3 /( (√(4−x^2 ))+x^2 −4)) dx

$\int \frac{x^{3}}{\sqrt{4 - x^{2}} + x^{2} - 4} d x$

Question Number 122397 Answers: 4 Comments: 0

a\∫((2x+1)/(1+x))(√((1−x)/(1+x)))dx c\∫(dx/( (√x)+(x)^(1/3) )) b\∫(dx/(x+(√(x−1)))) d\∫(dx/( (1+x)(√(1+x+x^2 ))))

$a ∖ \int \frac{2 x + 1}{1 + x} \sqrt{\frac{1 - x}{1 + x}} dx c ∖ \int \frac{dx}{\sqrt{x} + \sqrt[3]{x}}$ $b ∖ \int \frac{dx}{x + \sqrt{x - 1}} d ∖ \int \frac{dx}{(1 + x) \sqrt{1 + x + x^{2}}}$

Question Number 122366 Answers: 1 Comments: 0

Question Number 122349 Answers: 1 Comments: 1

Find the polynomial P(x) of least degree that has a maximum equal to 6 at x=1 and minimum equal to 2 at x=3.

$Find the polynomial P (x) of least degree$ $that has a maximum equal to 6 at x = 1$ $and minimum equal to 2 at x = 3 .$

Question Number 122330 Answers: 2 Comments: 0

...advanced calculus... prove that : Re(∫_0 ^( (π/2)) sin^3 (x)ln(ln(cos(x)))dx) =^? ((ln(3)−2γ)/3) ✓

$. . . a d v a n c e d c a l c u l u s . . .$ $p r o v e t h a t :$ $R e (\int_{0}^{\frac{π}{2}} {s i n}^{3} (x) l n (l n (c o s (x))) d x)$ $\overset{?}{=} \frac{l n (3) - 2 γ}{3} ✓$

Question Number 122323 Answers: 1 Comments: 1

calculate A_n =∫_0 ^∞ (dx/((x^2 +1)(x^2 +2)....(x^2 +n))) wth n integr natural and n≥1

$calculate A_{n} = \int_{0}^{\infty} \frac{dx}{(x^{2} + 1) (x^{2} + 2) . . . . (x^{2} + n)}$ $wth n integr natural and n ⩾ 1$

Question Number 122298 Answers: 1 Comments: 0

...nice calculus... prove that : Σ_(n=1 ) ^∞ {((ζ(2n+1)−1)/(n+1))}=−γ+ln(2)✓ ..m.n.1970..

$. . . n i c e c a l c u l u s . . .$ $p r o v e t h a t :$ $\underset{n = 1}{\sum^{\infty}} {\frac{ζ (2 n + 1) - 1}{n + 1}} = - γ + l n (2) ✓$ $. . m . n . 1970 . .$

Question Number 122290 Answers: 1 Comments: 1

... nice calculus... calculate :: Ω=∫_0 ^( 1) x^2 (ψ(1+x)−ψ(2−x))dx=??? .m.n.1970.

$. . . n i c e c a l c u l u s . . .$ $c a l c u l a t e ::$ $Ω = \int_{0}^{1} x^{2} (ψ (1 + x) - ψ (2 - x)) d x = ? ? ?$ $. m . n . 1970 .$

Question Number 122274 Answers: 2 Comments: 0

∫ ((√(1−(√x)))/( (√(1+(√x))))) dx ?

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

Question Number 122205 Answers: 1 Comments: 2

find ∫ (dx/(x(x+1)(√(x^2 +x))))

$find \int \frac{dx}{x (x + 1) \sqrt{x^{2} + x}}$

Question Number 122186 Answers: 2 Comments: 0

Obtain a reduction formulae for I_n = ∫_0 ^1 (ln x)^n dx find I_2 = ∫_0 ^1 (ln x)^2 dx

$Obtain a reduction formulae for$ $I_{n} = \underset{0}{\int^{1}} {(\ln x)}^{n} d x$ $find I_{2} = \underset{0}{\int^{1}} {(\ln x)}^{2} d x$

Question Number 122160 Answers: 1 Comments: 0

Question Number 122159 Answers: 3 Comments: 0

... nice calculus... prove that:: Ω=∫_0 ^( (π/2)) {tan^(−1) (ptan(x))−tan^(−1) (qtan(x))}(tan(x)+cot(x))dx =(π/2) log((p/q)) ( p , q >0 ) m.n.

$. . . n i c e c a l c u l u s . . .$ $p r o v e t h a t ::$ $Ω = \int_{0}^{\frac{π}{2}} {{t a n}^{- 1} (p t a n (x)) - {t a n}^{- 1} (q t a n (x))} (t a n (x) + c o t (x)) d x$ $= \frac{π}{2} l o g (\frac{p}{q}) (p, q > 0)$ $m . n .$

Question Number 122157 Answers: 2 Comments: 1

find ∫_(−1) ^1 (√(1+x^4 ))dx

$find \int_{- 1}^{1} \sqrt{1 + x^{4}} dx$

Pg 116 Pg 117 Pg 118 Pg 119 Pg 120 Pg 121 Pg 122 Pg 123 Pg 124 Pg 125

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