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solve ∫∫_G (7x−y)dxdy, where G is given by y=0 x+2y=3, x=y^2 i want to know if the integral below is a correct representation of the integral above. (∫_0 ^(3/2) ∫_0 ^(9/4) (7x−y)dxdy).

$s o l v e \int \int_{G} (7 x - y) d x d y, w h e r e G i s g i v e n b y y = 0$ $x + 2 y = 3, x = y^{2}$ $i w a n t t o k n o w i f t h e i n t e g r a l b e l o w i s a c o r r e c t$ $r e p r e s e n t a t i o n o f t h e i n t e g r a l a b o v e .$ $(\underset{0}{\int^{\frac{3}{2}}} \underset{0}{\int^{\frac{9}{4}}} (7 x - y) d x d y) .$

Question Number 130053 Answers: 4 Comments: 0

Show that ∫_0 ^( ∞) ((x^2 ln(x))/(x^4 +x^2 +1))dx = (π^2 /(12))

$Show that$ $\int_{0}^{\infty} \frac{x^{2} \ln (x)}{x^{4} + x^{2} + 1} dx = \frac{π^{2}}{12}$

Question Number 130029 Answers: 1 Comments: 2

1) decompose F(x)=(1/((x^2 −4)^3 (x^2 +1)^2 )) 2) find ∫_3 ^∞ (dx/((x^2 −4)^3 (x^2 +1)^2 ))

$1) decompose F (x) = \frac{1}{{(x^{2} - 4)}^{3} {(x^{2} + 1)}^{2}}$ $2) find \int_{3}^{\infty} \frac{dx}{{(x^{2} - 4)}^{3} {(x^{2} + 1)}^{2}}$

Question Number 130011 Answers: 2 Comments: 0

... advanced calculus... prove that:: Φ=∫_( R) e^((−e^x +2x)) x^2 dx=(1−γ)^2 +((π^2 −6)/6)

$. . . a d v a n c e d c a l c u l u s . . .$ $p r o v e t h a t ::$ $Φ = \int_{R} e^{(- e^{x} + 2 x)} x^{2} d x = {(1 - γ)}^{2} + \frac{π^{2} - 6}{6}$

Question Number 129996 Answers: 0 Comments: 0

∫((x^2 )^(1/5) /( ((1+(√x^5 )))^(1/3) ))dx

$\int \frac{\sqrt[5]{x^{2}}}{\sqrt[3]{1 + \sqrt{x^{5}}}} d x$

Question Number 129991 Answers: 0 Comments: 0

∫ (e^x )(((x^6 +x^5 +5x^4 )/((1+x)^6 )))dx = ...

$\int (e^{x}) (\frac{x^{6} + x^{5} + 5 x^{4}}{{(1 + x)}^{6}}) dx = . . .$

Question Number 129989 Answers: 1 Comments: 0

Find the area bounded xy^2 = 4a^2 (2a−x) and its asymptotes.

$Find the area bounded {xy}^{2} = {4 a}^{2} (2 a - x)$ $and its asymptotes .$

Question Number 129978 Answers: 1 Comments: 0

is this true for n∈N^★ ? someone please prove or falsify! ∫_0 ^∞ e^(−x^(2n) ) dx=Γ ((2n+1)/(2n))

$is this true for n \in N^{★} ? someone please prove$ $or falsify!$ $\underset{0}{\int^{\infty}} e^{- x^{2 n}} d x = Γ \frac{2 n + 1}{2 n}$

Question Number 129975 Answers: 2 Comments: 0

Question Number 129972 Answers: 1 Comments: 0

....nice calculus... evaluation: Ω=∫_0 ^( ∞) t^2 e^(−t) ln(t)dt=?? solution: f(s)=∫_0 ^( ∞) t^(2+s) e^(−t) dt Ω=f ′(0)=... f(s)=Γ(3+s) f ′(s)=Γ′(3+s)=ψ(3+s)Γ(3+s) f ′(0)=ψ(3)Γ(3)=2((3/2) −γ) =3−2γ ∴ Ω=∫_0 ^( ∞) t^2 e^(−t) ln(t)=3−2γ ...

$. . . . n i c e c a l c u l u s . . .$ $e v a l u a t i o n :$ $Ω = \int_{0}^{\infty} t^{2} e^{- t} l n (t) d t = ? ?$ $s o l u t i o n :$ $f (s) = \int_{0}^{\infty} t^{2 + s} e^{- t} d t$ $Ω = f^{'} (0) = . . .$ $f (s) = Γ (3 + s)$ $f^{'} (s) = Γ^{'} (3 + s) = ψ (3 + s) Γ (3 + s)$ $f^{'} (0) = ψ (3) Γ (3) = 2 (\frac{3}{2} - γ)$ $= 3 - 2 γ$ $∴ Ω = \int_{0}^{\infty} t^{2} e^{- t} l n (t) = 3 - 2 γ . . .$

Question Number 129946 Answers: 1 Comments: 0

∫ ((tan ϕ+3)/(sin ϕ)) dϕ ?

$\int \frac{\tan φ + 3}{\sin φ} d φ ?$

Question Number 129926 Answers: 1 Comments: 0

...nice calculus... evaluate: Σ_(k=0) ^∞ Σ_(m=0) ^∞ Σ_(n=0) ^∞ ((1/((k+m+n)!)))=?

$. . . n i c e c a l c u l u s . . .$ $e v a l u a t e :$ $\underset{k = 0}{\sum^{\infty}} \underset{m = 0}{\sum^{\infty}} \underset{n = 0}{\sum^{\infty}} (\frac{1}{(k + m + n)!}) = ?$

Question Number 129921 Answers: 3 Comments: 0

∫(1/((1−u^2 )^2 u^5 ))du=?? please...

$\int \frac{1}{{(1 - u^{2})}^{2} u^{5}} du = ? ?$ $please . . .$

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