Question and Answers Forum

IntegrationQuestion and Answers: Page 131

Question Number 116903 Answers: 2 Comments: 0

Question Number 116846 Answers: 0 Comments: 2

...nice calculus... prove that :: ∫_0 ^( (π/2)) (√(((2^x −1)sin^3 (x))/((2^x +1)(sin^3 (x)+cos^3 (x))))) dx<(π/8) ...m.n.1970...

$. . . n i c e c a l c u l u s . . .$ $p r o v e t h a t ::$ $\int_{0}^{\frac{π}{2}} \sqrt{\frac{(2^{x} - 1) {s i n}^{3} (x)}{(2^{x} + 1) ({s i n}^{3} (x) + {c o s}^{3} (x))}} d x < \frac{π}{8}$ $. . . m . n . 1970 . . .$

Question Number 116844 Answers: 1 Comments: 0

∫ ((8x+sin^(−1) (2x))/( (√(1−4x^2 )))) dx

$\int \frac{8 x + \sin^{- 1} (2 x)}{\sqrt{1 - {4 x}^{2}}} dx$

Question Number 116815 Answers: 2 Comments: 0

∫ (dx/((x−2)(x^2 +4))) =?

$\int \frac{dx}{(x - 2) (x^{2} + 4)} = ?$

Question Number 116813 Answers: 2 Comments: 0

∫_1 ^(√3) ((√(1+x^2 ))/x^2 ) dx ?

$\underset{1}{\int^{\sqrt{3}}} \frac{\sqrt{1 + x^{2}}}{x^{2}} dx ?$

Question Number 116803 Answers: 0 Comments: 0

Solve for X(x,y,z), Y(x,y,z), Z(x,y,z) { (((∂Z/∂y)−(∂Y/∂z)=1−x^2 )),(((∂Z/∂x)−(∂X/∂z)=−(y^2 /2))),(((∂Y/∂x)−(∂X/∂y)=z(2x−y))) :} where { ((X(x,y,0)=0)),((Y(x,y,0)=0)),((Z(x,y,z)=0)) :}

$Solve for X (x, y, z), Y (x, y, z), Z (x, y, z)$ ${\begin{cases} \frac{\partial Z}{\partial y} - \frac{\partial Y}{\partial z} = 1 - x^{2} \\ \frac{\partial Z}{\partial x} - \frac{\partial X}{\partial z} = - \frac{y^{2}}{2} \\ \frac{\partial Y}{\partial x} - \frac{\partial X}{\partial y} = z (2 x - y) \end{cases} where {\begin{cases} X (x, y, 0) = 0 \\ Y (x, y, 0) = 0 \\ Z (x, y, z) = 0 \end{cases}$

Question Number 116806 Answers: 2 Comments: 0

Hi Prove that: ∫_(-∞) ^(+∞) -e^(-x^2 ) dx=(√π) Thanks beforehand

$Hi$ $Prove that :$ $\int_{- \infty}^{+ \infty} - e^{- x^{2}} dx = \sqrt{π}$ $Thanks beforehand$

Question Number 116796 Answers: 1 Comments: 0

... calculus ... prove that :: ∫_0 ^( 1) (((1−x^p )(1−x^q )x^(r−1) )/(log(x)))dx=^(???) log( (((p+q+r+1)r)/((p+r)(q+r))) ) m.n.1970

$. . . c a l c u l u s . . .$ $p r o v e t h a t ::$ $\int_{0}^{1} \frac{(1 - x^{p}) (1 - x^{q}) x^{r - 1}}{l o g (x)} d x \overset{? ? ?}{=} l o g (\frac{(p + q + r + 1) r}{(p + r) (q + r)})$ $m . n . 1970$

Question Number 116744 Answers: 4 Comments: 0

... (( nice)/(calculus)) ... prove that :: ∫_(−1) ^( ∞) (e^(−4x) /( (√(x+1)))) dx =((√π)/2) e^4 ... m.n .1970...

$. . . \frac{n i c e}{c a l c u l u s} . . .$ $p r o v e t h a t ::$ $\int_{- 1}^{\infty} \frac{e^{- 4 x}}{\sqrt{x + 1}} d x = \frac{\sqrt{π}}{2} e^{4}$ $. . . m . n . 1970 . . .$

Question Number 116742 Answers: 0 Comments: 0

the curve y=f(x) is rotated about the x−axis to form solid.the volume of this solid is 0.5π(a−2sina cosa) for the limit of 0≤x≤a. find the value of a

$t h e c u r v e y = f (x) i s r o t a t e d a b o u t t h e$ $x - a x i s t o f o r m s o l i d . t h e v o l u m e o f t h i s$ $s o l i d i s 0.5 π (a - 2 s i n a c o s a) f o r t h e l i m i t$ $o f 0 ⩽ x ⩽ a . f i n d t h e v a l u e o f a$

Question Number 116738 Answers: 1 Comments: 1

determine the area of the region bounded by y=(2x+6)^(0.5 ) and y=x−1

$d e t e r m i n e t h e a r e a o f t h e r e g i o n b o u n d e d$ $b y y = {(2 x + 6)}^{0.5} a n d y = x - 1$

Question Number 116737 Answers: 1 Comments: 0

find the lenght of the function y=sinx for 0<x<π

$f i n d t h e l e n g h t o f t h e f u n c t i o n y = s i n x$ $f o r 0 < x < π$

Question Number 116710 Answers: 2 Comments: 0

Question Number 116701 Answers: 2 Comments: 2

∫ (dx/(x+x(√x))) =?

$\int \frac{dx}{x + x \sqrt{x}} = ?$

Question Number 116687 Answers: 2 Comments: 0

Help please, to solve this ... If f(x)=1+x^2 for x∈[−2,2] and f(x)=5 otherwise. Then what is the value of ∫_(−2) ^(+2) f(2x^2 )dx?

$H e l p p l e a s e, t o s o l v e t h i s . . .$ $I f f (x) = 1 + x^{2} f o r x \in [- 2, 2] a n d$ $f (x) = 5 o t h e r w i s e .$ $T h e n w h a t i s t h e v a l u e o f$ $\int_{- 2}^{+ 2} f (2 x^{2}) d x ?$

Question Number 116672 Answers: 2 Comments: 0

... nice calculus ... prove that : I = ∫_0 ^( 1) ((π/4) −Arctan(x))(dx/(1−x^2 )) = (G/2) ✓ G is catalan constant ... M.N.1970

$. . . n i c e c a l c u l u s . . .$ $p r o v e t h a t :$ $I = \int_{0}^{1} (\frac{π}{4} - A r c t a n (x)) \frac{d x}{1 - x^{2}} = \frac{G}{2} ✓$ $G i s c a t a l a n c o n s t a n t . . .$ $M . N . 1970$

Question Number 116667 Answers: 1 Comments: 0

... nice calculus... very nice integral:: demonstrate::: Ω = ∫_0 ^( 1) ((1−x)/((1+x+x^2 +x^3 )log(x))) dx=^(???) log((√(1/2))) .m.n.1970.

$. . . n i c e c a l c u l u s . . .$ $v e r y n i c e i n t e g r a l ::$ $d e m o n s t r a t e :::$ $Ω = \int_{0}^{1} \frac{1 - x}{(1 + x + x^{2} + x^{3}) l o g (x)} d x \overset{? ? ?}{=} l o g (\sqrt{\frac{1}{2}})$ $. m . n . 1970 .$

Question Number 116763 Answers: 0 Comments: 1

∫(dx/( ((1+x^3 ))^(1/3) ))=?

$\int \frac{d x}{\sqrt[3]{1 + x^{3}}} = ?$

Question Number 116717 Answers: 2 Comments: 0

∫xdx

$\int x d x$

Question Number 116627 Answers: 2 Comments: 0

... nice calculus... please evaluate :: Φ = (((∫_0 ^( (π/2)) ((e^x +e^(−x) )/(sin(x)+cos(x)))dx)^2 )/((∫_0 ^( (π/2)) (e^x /(sin(x)+cos(x)))dx)(∫_0 ^( (π/2)) (e^(−x) /(sin(x)+cos(x)))dx))) =??? m.n.1970

$. . . n i c e c a l c u l u s . . .$ $p l e a s e e v a l u a t e ::$ $Φ = \frac{{(\int_{0}^{\frac{π}{2}} \frac{e^{x} + e^{- x}}{s i n (x) + c o s (x)} d x)}^{2}}{(\int_{0}^{\frac{π}{2}} \frac{e^{x}}{s i n (x) + c o s (x)} d x) (\int_{0}^{\frac{π}{2}} \frac{e^{- x}}{s i n (x) + c o s (x)} d x)} = ? ? ?$ $m . n . 1970$

Question Number 116626 Answers: 2 Comments: 0

Π_(n=1) ^∞ (((a^2 n^2 )/((an)^2 −1))))=???

$\underset{n = 1}{\prod^{\infty}} (\frac{a^{2} n^{2}}{{(a n)}^{2} - 1)}) = ? ? ?$

Question Number 116590 Answers: 2 Comments: 0

∫ ((√x)/(1+x^3 )) dx =?

$\int \frac{\sqrt{x}}{1 + x^{3}} dx = ?$

Question Number 116586 Answers: 0 Comments: 0

1) explicite ∫_0 ^∞ ((arctan(1+x(2+t^2 )))/(2+t^2 ))dt withx>0 2)determine values of ∫_0 ^∞ ((arctan(3+t^2 ))/(2+t^2 ))dt and ∫_0 ^∞ ((arctan(5+2t^2 ))/(2+t^2 ))dt

$1) e x p l i c i t e \int_{0}^{\infty} \frac{a r c t a n (1 + x (2 + t^{2}))}{2 + t^{2}} d t$ $w i t h x > 0$ $2) d e t e r m i n e v a l u e s o f$ $\int_{0}^{\infty} \frac{a r c t a n (3 + t^{2})}{2 + t^{2}} d t a n d$ $\int_{0}^{\infty} \frac{a r c t a n (5 + 2 t^{2})}{2 + t^{2}} d t$

Question Number 116564 Answers: 2 Comments: 0

∫ (dx/(x+(x)^(1/(3 )) )) ?

$\int \frac{dx}{x + \sqrt[3]{x}} ?$

Question Number 116560 Answers: 1 Comments: 1

if arctan(x+iy) =a+ib with a and b reals determine a and b

$i f a r c t a n (x + i y) = a + i b$ $w i t h a a n d b r e a l s d e t e r m i n e$ $a a n d b$

Question Number 116557 Answers: 2 Comments: 0

calculate ∫_0 ^∞ ((ln(1+x(1+t^2 ))/(1+t^2 )) dt with x>0 2) find the value of ∫_0 ^∞ ((ln(2+t^2 ))/(1+t^2 ))dt and ∫_0 ^∞ ((ln(3+2t^2 ))/(1+t^2 ))dt

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

Pg 126 Pg 127 Pg 128 Pg 129 Pg 130 Pg 131 Pg 132 Pg 133 Pg 134 Pg 135

Contact: info@tinkutara.com