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IntegrationQuestion and Answers: Page 54

Question Number 159823 Answers: 2 Comments: 0

Question Number 159768 Answers: 1 Comments: 1

Question Number 159693 Answers: 1 Comments: 0

Ω:=∫_1 ^( 10) x d (x + ⌊ x ⌋) =?

$Ω := \int_{1}^{10} x d (x + ⌊ x ⌋) = ?$

Question Number 159682 Answers: 3 Comments: 0

∫_( 0) ^( (π/2)) ((cos x sin x)/(cos x + sin x)) dx =?

$\int_{0}^{\frac{π}{2}} \frac{\cos x \sin x}{\cos x + \sin x} d x = ?$

Question Number 159681 Answers: 1 Comments: 0

prove that : P= Π_(n=1) ^∞ (1−(1/(n(n+2))) ) =^? ((−(√2) sin(π(√2) ))/π) m.n

$p r o v e t h a t :$ $P = \underset{n = 1}{\prod^{\infty}} (1 - \frac{1}{n (n + 2)}) \overset{?}{=} \frac{- \sqrt{2} s i n (π \sqrt{2})}{π}$ $m . n$

Question Number 159680 Answers: 0 Comments: 2

∫_( 0) ^( (π/6)) ((sin x sin (x+60°) sin (x+120°))/(cos 3x + sin 3x)) dx=?

$\int_{0}^{\frac{π}{6}} \frac{\sin x \sin (x + 60 °) \sin (x + 120 °)}{\cos 3 x + \sin 3 x} d x = ?$

Question Number 159671 Answers: 1 Comments: 0

∫ _0 ^∞ ((sin^2 (x)−xsin(x))/x^3 ) dx

$\int \underset{0}{\overset{\infty}{}} \frac{\sin^{2} (x) - x \sin (x)}{x^{3}} d x$

Question Number 159612 Answers: 2 Comments: 0

Question Number 159597 Answers: 1 Comments: 0

Question Number 159552 Answers: 1 Comments: 4

Question Number 159561 Answers: 0 Comments: 0

Question Number 159315 Answers: 0 Comments: 1

∫ (dx/( (((x−1)^3 (x+2)^5 ))^(1/4) )) ?

$\int \frac{d x}{\sqrt[4]{{(x - 1)}^{3} {(x + 2)}^{5}}} ?$

Question Number 159297 Answers: 1 Comments: 1

Question Number 159233 Answers: 1 Comments: 0

Question Number 159226 Answers: 1 Comments: 0

Ω = ∫_0 ^∞ (((x^5 )^(1/6) −(√x))/((1+x^2 ) ln x)) dx =?

$Ω = \int_{0}^{\infty} \frac{\sqrt[6]{x^{5}} - \sqrt{x}}{(1 + x^{2}) \ln x} d x = ?$

Question Number 159143 Answers: 1 Comments: 0

Question Number 159106 Answers: 0 Comments: 0

∫_0 ^π ((sin(nz))/(z^4 sin(πz)))dz

$\int_{0}^{π} \frac{\sin (n z)}{z^{4} \sin (π z)} d z$

Question Number 159080 Answers: 1 Comments: 0

Σ_(n=0) ^∞ (1/(n!(n^4 +n^2 +1)))=?

$\underset{n = 0}{\sum^{\infty}} \frac{1}{n! (n^{4} + n^{2} + 1)} = ?$

Question Number 159070 Answers: 1 Comments: 0

Ω:= ∫_0 ^( ∞) ( H_( (i/x)) + H_( −(i/x)) ) dx=?

$Ω := \int_{0}^{\infty} (H_{\frac{i}{x}} + H_{- \frac{i}{x}}) d x = ?$

Question Number 159069 Answers: 0 Comments: 0

Question Number 159008 Answers: 1 Comments: 0

∫(6^x /(4^x +9^x ))dx=?

$\int \frac{6^{x}}{4^{x} + 9^{x}} d x = ?$

Question Number 158993 Answers: 0 Comments: 0

∫_0 ^1 ∫_0 ^1 xye^(x^2 y^2 ) dxdy=?

$\int_{0}^{1} \int_{0}^{1} {xye}^{x^{2} y^{2}} dxdy = ?$

Question Number 158990 Answers: 0 Comments: 0

∫ ((sec x)/(sin x+csc x−1)) dx=?

$\int \frac{\sec x}{\sin x + \csc x - 1} d x = ?$

Question Number 158973 Answers: 1 Comments: 0

Question Number 158965 Answers: 2 Comments: 0

∫ ((√(1+x))/( (√x) +1)) dx =?

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

Question Number 158922 Answers: 0 Comments: 0

∫e^(sec x) sec^3 x(sin^2 x+cos x+sin x+sin x cos x)dx=?

$\int e^{\sec x} \sec^{3} x (\sin^{2} x + \cos x + \sin x + \sin x \cos x) d x = ?$

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