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IntegrationQuestion and Answers: Page 27

Question Number 188982 Answers: 0 Comments: 2

Question Number 188889 Answers: 1 Comments: 0

If, y= (( Arcsin((√x) ))/( (√( x (1−x ))))) ⇒ y′ .p(x) + y .q(x)= 1 find , ∫_0 ^( 1) p(x).q(x)dx=? p , q are two pllynomils...

$I f, y = \frac{A r c s i n (\sqrt{x})}{\sqrt{x (1 - x)}} \Rightarrow$ $y^{'} . p (x) + y . q (x) = 1$ $f i n d, \int_{0}^{1} p (x) . q (x) d x = ?$ $p, q a r e t w o p l l y n o m i l s . . .$

Question Number 188861 Answers: 2 Comments: 0

Question Number 188552 Answers: 0 Comments: 1

Question Number 188511 Answers: 0 Comments: 0

evaluate ∫_0 ^π (dx/(a+bcosx )) , a > 0 and deduce that ∫_0 ^π (dx/((a+bcos x)^2 )) = ((πa)/((a^2 −b^2 )^(3/2) )) ; a^2 >b^2 and ∫_0 ^π ((cos x dx)/((a+bcos x)^2 )) = ((−πb)/((a^2 −b^2 )^(3/2) )) ; a^2 >b^2

$e v a l u a t e$ $\int_{0}^{π} \frac{d x}{a + b \cos x}, a > 0$ $a n d d e d u c e t h a t$ $\int_{0}^{π} \frac{d x}{{(a + b \cos x)}^{2}} = \frac{π a}{{(a^{2} - b^{2})}^{3 / 2}}; a^{2} > b^{2}$ $a n d \int_{0}^{π} \frac{\cos x d x}{{(a + b \cos x)}^{2}} = \frac{- π b}{{(a^{2} - b^{2})}^{3 / 2}}; a^{2} > b^{2}$

Question Number 188470 Answers: 0 Comments: 0

∫_0 ^(π/4) arctan((√((1−tan^2 x)/2)))dx = ?

$\underset{0}{\int^{π / 4}} a r c t a n (\sqrt{\frac{1 - {t a n}^{2} x}{2}}) d x = ?$

Question Number 188384 Answers: 1 Comments: 0

if ∫_0 ^∞ e^(−ax) dx = (1/a) show that ∫_0 ^∞ e^(−ax) x^n dx = ((n!)/a^(n+1) )

$if \int_{0}^{\infty} e^{- a x} d x = \frac{1}{a}$ $s h o w t h a t \int_{0}^{\infty} e^{- a x} x^{n} d x = \frac{n!}{a^{n + 1}}$

Question Number 188381 Answers: 2 Comments: 0

Advanced calculus Find the value of the following series. Ω = Σ_(n=1) ^∞ (( (−1)^( n) ζ ( n ))/(n. 2^( n) )) = ? ζ ( z ) = Σ_( n=1) ^∞ (( 1)/(n^( z) )) ; Re ( z )>1

$Advanced calculus$ $Find the value of the following series .$ $Ω = \underset{n = 1}{\sum^{\infty}} \frac{{(- 1)}^{n} ζ (n)}{n . 2^{n}} = ?$ $ζ (z) = \underset{n = 1}{\sum^{\infty}} \frac{1}{n^{z}}; R e (z) > 1$

Question Number 188380 Answers: 1 Comments: 0

Question Number 188192 Answers: 2 Comments: 0

prove that ∫_0 ^∞ e^(−a^2 x^2 ) cos(2bx) dx = ((√π)/(2a))e^(−b^2 /a^2 )

$p r o v e t h a t$ $\int_{0}^{\infty} e^{- a^{2} x^{2}} \cos (2 b x) d x = \frac{\sqrt{π}}{2 a} e^{- b^{2} / a^{2}}$

Question Number 188164 Answers: 1 Comments: 1

Question Number 188086 Answers: 1 Comments: 0

I = ∫_0 ^∞ ((tan^(−1) (x/a))/(x(x^2 +b^2 )))dx

$I = \int_{0}^{\infty} \frac{\tan^{- 1} (x / a)}{x (x^{2} + b^{2})} d x$

Question Number 188036 Answers: 1 Comments: 0

∫2^x e^x dx

$\int 2^{x} e^{x} d x$

Question Number 188035 Answers: 1 Comments: 0

solve ∫(x^2 /((a+bx)^2 ))dx

$s o l v e$ $\int \frac{x^{2}}{{(a + b x)}^{2}} d x$

Question Number 188034 Answers: 1 Comments: 0

solve ∫((x^2 +3)/(x^6 (x^2 +1)))dx

$s o l v e$ $\int \frac{x^{2} + 3}{x^{6} (x^{2} + 1)} d x$

Question Number 187993 Answers: 0 Comments: 0

prove that ∫_0 ^(π/2) ∫_0 ^(π/2) (((sin3x)/(sin2y)))^(1/3) dxdy=(π/(2(√3)))

$p r o v e t h a t$ $\int_{0}^{\frac{π}{2}} \int_{0}^{\frac{π}{2}} \sqrt[3]{\frac{s i n 3 x}{s i n 2 y}} d x d y = \frac{π}{2 \sqrt{3}}$

Question Number 187898 Answers: 2 Comments: 0

∫ ((1−cos x)/(cos x+sin x−1)) dx=?

$\int \frac{1 - \cos x}{\cos x + \sin x - 1} dx = ?$

Question Number 187890 Answers: 1 Comments: 0

Question Number 187855 Answers: 2 Comments: 0

solve ∫((x^4 +x^2 +1)/(2(x^2 +1)))dx

$s o l v e$ $\int \frac{x^{4} + x^{2} + 1}{2 (x^{2} + 1)} d x$

Question Number 187703 Answers: 2 Comments: 0

∫ (1/(5x^2 − 2x − 4)) dx

$\int \frac{1}{{5 x}^{2} - 2 x - 4} dx$

Question Number 187700 Answers: 0 Comments: 1

Find minimum area of the part y=x^2 and y=kx(x^2 −k), k>0

$F i n d m i n i m u m a r e a o f t h e p a r t$ $y = x^{2} a n d y = k x (x^{2} - k), k > 0$

Question Number 187602 Answers: 1 Comments: 0

∫_(1/4) ^(1/2) ((sin^(−1) ((√x))−cos^(−1) ((√x)))/(sin^(−1) ((√x))+cos^(−1) ((√x)))) dx=?

$\underset{1 / 4}{\int^{1 / 2}} \frac{\sin^{- 1} (\sqrt{x}) - \cos^{- 1} (\sqrt{x})}{\sin^{- 1} (\sqrt{x}) + \cos^{- 1} (\sqrt{x})} d x = ?$

Question Number 187531 Answers: 3 Comments: 0

∫_0 ^∞ x^2 e^(−x) dx=?

$\underset{0}{\int^{\infty}} x^{2} e^{- x} d x = ?$

Question Number 187530 Answers: 1 Comments: 0

∫(dx/( (√(a^2 +be^(cx) ))))=?

$\int \frac{d x}{\sqrt{a^{2} + {b e}^{c x}}} = ?$

Question Number 187529 Answers: 1 Comments: 0

∫x^2 ∙sin^(−1) (x)dx=?

$\int x^{2} \cdot {s i n}^{- 1} (x) d x = ?$

Question Number 187528 Answers: 1 Comments: 0

∫_((9π)/2) ^((7π)/(1.5)) (dx/( (√(1−sinx))))=?

$\underset{\frac{9 π}{2}}{\int^{\frac{7 π}{1.5}}} \frac{d x}{\sqrt{1 - s i n x}} = ?$

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