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IntegrationQuestion and Answers: Page 7

Question Number 214661 Answers: 1 Comments: 0

Question Number 214618 Answers: 1 Comments: 0

∫_0 ^(Π/2) ((3(√(tan x)))/((sin x+cos x)^2 ))dx

$\int_{0}^{Π / 2} \frac{3 \sqrt{\tan x}}{{(\sin x + \cos x)}^{2}} d x$

Question Number 214560 Answers: 1 Comments: 0

∫_1 ^( x) ((ln x)/( (√(1−(ln x)^2 ))))dx

$\int_{1}^{x} \frac{\ln x}{\sqrt{1 - {(\ln x)}^{2}}} d x$

Question Number 214509 Answers: 1 Comments: 4

Find the volume of the solid of revolution generated by rotating the area bounded by y=x(2−x) and y=x about the y−axis.

$Find the volume of the solid of revolution$ $generated by rotating the area bounded$ $by y = x (2 - x) and y = x about the y - axis .$

Question Number 214498 Answers: 1 Comments: 0

Question Number 214568 Answers: 1 Comments: 0

∫((b+ax)/(1+sin x)) dx

$\int \frac{b + a x}{1 + \sin x} d x$

Question Number 214360 Answers: 1 Comments: 0

Find ∫_(−∞) ^∞ e^(−ax^2 ) dx when a is constant without changing the coordinate.

$Find \underset{- \infty}{\int^{\infty}} e^{- {a x}^{2}} d x when a is constant without changing the coordinate .$

Question Number 214301 Answers: 1 Comments: 1

∫_0 ^(π/2) sin^2 (sin x)+ cos^2 (cos x) dx =?

$\underset{0}{\int^{\frac{π}{2}}} \sin^{2} (\sin x) + \cos^{2} (\cos x) dx = ?$

Question Number 213962 Answers: 1 Comments: 0

∫((x^4 −1)/(x(x^4 −5)(x^5 −5x+1)))dx

$\int \frac{x^{4} - 1}{x (x^{4} - 5) (x^{5} - 5 x + 1)} d x$

Question Number 213945 Answers: 3 Comments: 0

Question Number 213944 Answers: 1 Comments: 0

Question Number 213934 Answers: 0 Comments: 3

∫_(−π/2) ^( π/2) ∫_0 ^( R) (((dθ)(dr)(a+rcos θ))/((r^2 +a^2 +2arcos θ)^(3/2) )) =f(a,R) Find f(a, R).

$\int_{- π / 2}^{π / 2} \int_{0}^{R} \frac{(d θ) (d r) (a + r \cos θ)}{{(r^{2} + a^{2} + 2 a r \cos θ)}^{3 / 2}} = f (a, R)$ $F i n d f (a, R) .$

Question Number 213844 Answers: 3 Comments: 0

∫_(−1) ^1 ∫_0 ^(√(1−x^2 )) ∫_(√(x^2 +y^2 )) ^(√(2−x^2 −y^2 )) (√(x^2 +y^2 +z^2 )) dzdydx

$\int_{- 1}^{1} \int_{0}^{\sqrt{1 - x^{2}}} \int_{\sqrt{x^{2} + y^{2}}}^{\sqrt{2 - x^{2} - y^{2}}} \sqrt{x^{2} + y^{2} + z^{2}} d z d y d x$

Question Number 213776 Answers: 1 Comments: 0

Find the value of the following expression. Ω= (( Im( Li_2 (2)))/(∫_0 ^( (π/2)) ln(sin(x )) dx)) = ?

$F i n d t h e v a l u e o f t h e f o l l o w i n g$ $e x p r e s s i o n .$ $Ω = \frac{I m ({Li}_{2} (2))}{\int_{0}^{\frac{π}{2}} \ln (\sin (x)) d x} = ?$

Question Number 213759 Answers: 1 Comments: 0

Question Number 213738 Answers: 1 Comments: 0

Question Number 213735 Answers: 2 Comments: 0

Question Number 213724 Answers: 0 Comments: 1

Question Number 213662 Answers: 1 Comments: 0

Question Number 213660 Answers: 0 Comments: 0

prove that ... lim_(n→∞) ∫_0 ^( 3) (( x^2 (1−x )x^n )/(1+ x^(2n) )) dx=^? 0 −−−−−−−−−−−

$p r o v e t h a t . . .$ $\lim_{n \to \infty} \int_{0}^{3} \frac{x^{2} (1 - x) x^{n}}{1 + x^{2 n}} d x \overset{?}{=} 0$ $- - - - - - - - - - -$

Question Number 213659 Answers: 1 Comments: 0

∫_(−∞) ^∞ ((∣24x−24∣−20)/(22^x +22)) dx =?

$\underset{- \infty}{\int^{\infty}} \frac{∣ 24 x - 24 ∣ - 20}{22^{x} + 22} dx = ?$

Question Number 213656 Answers: 1 Comments: 0

Question Number 213652 Answers: 1 Comments: 0

Show that ∫xdx=(x^2 /x)+C.

$Show that \int x d x = \frac{x^{2}}{x} + C .$

Question Number 213628 Answers: 1 Comments: 0

Question Number 213423 Answers: 2 Comments: 0

⌊ (1/2)x−1⌋ + ⌊ (2/2)x−2⌋+⌊(3/2)x−3⌋+...+⌊((100)/2)x−100⌋ ≤10100 for x non negative integers. find the possible value of x

$⌊ \frac{1}{2} x - 1 ⌋ + ⌊ \frac{2}{2} x - 2 ⌋ + ⌊ \frac{3}{2} x - 3 ⌋ + . . . + ⌊ \frac{100}{2} x - 100 ⌋ ⩽ 10100$ $for x non negative integers .$ $find the possible value of x$

Question Number 213217 Answers: 1 Comments: 0

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