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IntegrationQuestion and Answers: Page 6

Question Number 215434 Answers: 0 Comments: 0

∫_0 ^( t) (√(t/(b−t))) e^t dt =?

$\int_{0}^{t} \sqrt{\frac{t}{b - t}} e^{t} d t = ?$

Question Number 215458 Answers: 1 Comments: 0

Evaluate lim_(n→∞) n^2 ∫_0 ^1 x^(n+1) sin(πx)dx

$Evaluate \lim_{n \to \infty} n^{2} \int_{0}^{1} x^{n + 1} \sin (π x) d x$

Question Number 215414 Answers: 1 Comments: 2

∫ ((sin^3 ((x/2))sec((x/2)))/( (√(cos^3 x + cos^2 x + cosx)))) dx Solve this integral.

$\int \frac{\sin^{3} (\frac{x}{2}) \sec (\frac{x}{2})}{\sqrt{\cos^{3} x + \cos^{2} x + \cos x}} d x$ $Solve this integral .$

Question Number 215404 Answers: 1 Comments: 0

∫_a ^( x) ((√(1+4x^2 ))/( (√(a^2 −x^2 ))))dx = ?

$\int_{a}^{x} \frac{\sqrt{1 + 4 x^{2}}}{\sqrt{a^{2} - x^{2}}} d x = ?$

Question Number 215393 Answers: 0 Comments: 1

∫_0 ^∞ (x^(2ν) /((x^2 +β^2 )^(μ+1) ))sin(ax)dx

$\int_{0}^{\infty} \frac{x^{2 ν}}{{(x^{2} + β^{2})}^{μ + 1}} \sin (a x) d x$

Question Number 215386 Answers: 1 Comments: 0

Question Number 215390 Answers: 1 Comments: 0

∮_γ x^2 dx [γ: x^2 +y^2 =1]

$\oint_{γ} x^{2} d x [γ : x^{2} + y^{2} = 1]$

Question Number 215344 Answers: 2 Comments: 0

Question Number 215315 Answers: 2 Comments: 0

Evaluate lim_(n→∞) ((1/(2n+1))+(1/(2n+2))+...+(1/(4n)))

$Evaluate \lim_{n \to \infty} (\frac{1}{2 n + 1} + \frac{1}{2 n + 2} + . . . + \frac{1}{4 n})$

Question Number 215280 Answers: 2 Comments: 2

volume of solids generated by revolving the region bounded by the curve and line the y-axis y=x ,y = x/2 ,x = 2

$v o l u m e o f s o l i d s g e n e r a t e d b y r e v o l v i n g$ $t h e r e g i o n b o u n d e d b y t h e c u r v e a n d l i n e$ $t h e y - a x i s$ $y = x, y = x / 2, x = 2$

Question Number 215190 Answers: 1 Comments: 0

∫(x^(p−1) /(1+x^n ))lnln(1/x)dx,p,n>0

$\int \frac{x^{p - 1}}{1 + x^{n}} lnln \frac{1}{x} d x, p, n > 0$

Question Number 215189 Answers: 1 Comments: 0

∫_0 ^∞ ((ln(1+x^(12) ))/(1+x^2 ))dx

$\int_{0}^{\infty} \frac{\ln (1 + x^{12})}{1 + x^{2}} d x$

Question Number 215188 Answers: 2 Comments: 0

∫_0 ^∞ ((x cos 2πx)/(e^(2π(√x)) −1))dx

$\int_{0}^{\infty} \frac{x \cos 2 π x}{e^{2 π \sqrt{x}} - 1} d x$

Question Number 215185 Answers: 1 Comments: 0

∫_(−∞) ^∞ ((exp(((ax)/(1+x^2 )))exp((a/(1+x^2 ))))/(1+x^2 ))dx,a>0

$\int_{- \infty}^{\infty} \frac{\exp (\frac{a x}{1 + x^{2}}) \exp (\frac{a}{1 + x^{2}})}{1 + x^{2}} d x, a > 0$

Question Number 215161 Answers: 1 Comments: 4

∫(((x^8 +16x^7 −2x^4 −3)e^x )/((1+x^4 )^(2/3) ))dx

$\int \frac{(x^{8} + 16 x^{7} - 2 x^{4} - 3) e^{x}}{{(1 + x^{4})}^{2 / 3}} d x$

Question Number 215134 Answers: 2 Comments: 0

Question Number 215091 Answers: 1 Comments: 0

Σ_(n=0) ^∞ (−1)^n (( Γ^( 2) (n+1))/(Γ (2n+1))) = ? −−− β (p ,q ) = (( Γ (p)Γ(q))/(Γ(p+q )))

$\underset{n = 0}{\sum^{\infty}} {(- 1)}^{n} \frac{Γ^{2} (n + 1)}{Γ (2 n + 1)} = ?$ $- - -$ $β (p, q) = \frac{Γ (p) Γ (q)}{Γ (p + q)}$

Question Number 215061 Answers: 1 Comments: 0

∫_0 ^( ∞) ∫_0 ^( ∞) e^( − (( x^2 +y^2 )/2)) sin(xy )dxdy=?

$\int_{0}^{\infty} \int_{0}^{\infty} e^{- \frac{x^{2} + y^{2}}{2}} \sin (x y) d x d y = ?$

Question Number 215020 Answers: 1 Comments: 2

f: [0 , 1] →R is given. f ′′ is continuous . by the way f(0)=f(1). prove that : determinant (((∫_0 ^( 1) ( f ′′ (x))^( 2) dx ≥ 3(f ′(1))^2 )))

$f : [0, 1] \to R i s g i v e n .$ $f^{″} i s c o n t i n u o u s .$ $b y t h e w a y f (0) = f (1) .$ $p r o v e t h a t :$ $\begin{matrix} \int_{0}^{1} {(f^{″} (x))}^{2} d x ⩾ 3 {(f^{'} (1))}^{2} \end{matrix}$

Question Number 215011 Answers: 0 Comments: 0

Question Number 214925 Answers: 2 Comments: 1

Question Number 214917 Answers: 2 Comments: 0

Question Number 214915 Answers: 2 Comments: 0

Question Number 214770 Answers: 1 Comments: 0

∫sin^3 xdx=?

$\int \sin^{3} x d x = ?$

Question Number 214756 Answers: 2 Comments: 0

∫(1/(2(√x)))sin (√x)dx=?

$\int \frac{1}{2 \sqrt{x}} \sin \sqrt{x} d x = ?$

Question Number 214750 Answers: 1 Comments: 0

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