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IntegrationQuestion and Answers: Page 117

Question Number 124785 Answers: 0 Comments: 0

∫_( 0) ^( a) ∫_( 0) ^( (√(a^2 −x^2 ))) (1/((1+e^y )(√(a^2 −x^2 −y^2 ))))dxdy

$\int_{0}^{a} \int_{0}^{\sqrt{a^{2} - x^{2}}} \frac{1}{(1 + e^{y}) \sqrt{a^{2} - x^{2} - y^{2}}} dxdy$

Question Number 124794 Answers: 1 Comments: 0

If f(x)= { ((2x ; 0<x<1)),((3 ; x=1 )),((6x−1 ; 1<x<2)) :} find ∫_0 ^2 f(x) dx ?

$I f f (x) = {\begin{cases} 2 x; 0 < x < 1 \\ 3; x = 1 \\ 6 x - 1; 1 < x < 2 \end{cases}$ $f i n d \underset{0}{\int^{2}} f (x) d x ?$

Question Number 124853 Answers: 2 Comments: 0

∫_1 ^( x^3 +5x) f(t) dt = 2x then f(18) =?

$\int_{1}^{x^{3} + 5 x} f (t) d t = 2 x$ $t h e n f (18) = ?$

Question Number 124742 Answers: 0 Comments: 2

∫((3^t +11)/(6^t +11))dt collected problem

$\int \frac{3^{t} + 11}{6^{t} + 11} d t c o l l e c t e d p r o b l e m$

Question Number 124738 Answers: 0 Comments: 3

...nice calculus... simple limit:: lim_(n→∞) {((1^(a+1) +2^(a+1) +...+n^(a+1) )/(n(1^a +2^a +....n^a )))}=? where a ≠−2 , −1

$. . . n i c e c a l c u l u s . . .$ $s i m p l e l i m i t ::$ ${l i m}_{n \to \infty} {\frac{1^{a + 1} + 2^{a + 1} + . . . + n^{a + 1}}{n (1^{a} + 2^{a} + . . . . n^{a})}} = ?$ $w h e r e a \neq - 2, - 1$

Question Number 124675 Answers: 0 Comments: 1

∫_1 ^3 (x−1)^3 (3−x)^2 dx

$\int_{1}^{3} {(x - 1)}^{3} {(3 - x)}^{2} d x$

Question Number 124672 Answers: 1 Comments: 1

∫_(−3) ^(−2) (y+3)^6 (y+2)^4 dy

$\int_{- 3}^{- 2} {(y + 3)}^{6} {(y + 2)}^{4} d y$

Question Number 124654 Answers: 3 Comments: 1

∫_(1/(√2)) ^(1/2) (e^(cos^(−1) (x)) /( (√(1−x^2 )))) dx ?

$\underset{1 / \sqrt{2}}{\int^{1 / 2}} \frac{e^{\cos^{- 1} (x)}}{\sqrt{1 - x^{2}}} d x ?$

Question Number 124644 Answers: 2 Comments: 0

∫_(2/(√3)) ^2 ((cos (sec^(−1) x))/(x(√(x^2 −1)))) dx ∫_( (√2)) ^2 ((sec^2 (sec^(−1) x))/(x(√(x^2 −1)))) dx

$\underset{2 / \sqrt{3}}{\int^{2}} \frac{\cos (\sec^{- 1} x)}{x \sqrt{x^{2} - 1}} d x$ $\underset{\sqrt{2}}{\int^{2}} \frac{\sec^{2} (\sec^{- 1} x)}{x \sqrt{x^{2} - 1}} d x$

Question Number 124632 Answers: 3 Comments: 0

Calculate ∫_0 ^2 (√((2+x)/(2−x))) dx

$C a l c u l a t e \underset{0}{\int^{2}} \sqrt{\frac{2 + x}{2 - x}} d x$

Question Number 124624 Answers: 1 Comments: 0

∫ (dx/( (x)^(1/3) +4x))

$\int \frac{d x}{\sqrt[3]{x} + 4 x}$

Question Number 124608 Answers: 2 Comments: 0

∫_0 ^∞ sinx^p dx ∫_0 ^∞ ((sinx^p )/x^q )dx collected question

$\int_{0}^{\infty} {s i n x}^{p} d x$ $\int_{0}^{\infty} \frac{{s i n x}^{p}}{x^{q}} d x$ $c o l l e c t e d q u e s t i o n$

Question Number 124607 Answers: 2 Comments: 0

∫(dx/((x^3 +1)^2 )) = ?

$\int \frac{d x}{{(x^{3} + 1)}^{2}} = ?$

Question Number 124594 Answers: 1 Comments: 1

Show that ∫_0 ^(ln 2) (1/(cosh(x + ln 4))) dx = 2 tan^(−1) ((4/(33)))

$Show that$ $\int_{0}^{\ln 2} \frac{1}{\cosh (x + \ln 4)} d x = 2 \tan^{- 1} (\frac{4}{33})$

Question Number 124587 Answers: 1 Comments: 0

...nice ◂::::▶ calculus simple question:: prove that :: ∫_0 ^( ∞) (4/( (√(4+x^4 )))) dx=^(???) ∫_0 ^( (π/2)) (dx/( (√(sin(x))))) +∫_0 ^( (π/2)) (dx/( (√(cos(x)))))

$. . . n i c e ◂ :::: ▸ c a l c u l u s$ $s i m p l e q u e s t i o n ::$ $p r o v e t h a t ::$ $\int_{0}^{\infty} \frac{4}{\sqrt{4 + x^{4}}} d x \overset{? ? ?}{=} \int_{0}^{\frac{π}{2}} \frac{d x}{\sqrt{s i n (x)}} + \int_{0}^{\frac{π}{2}} \frac{d x}{\sqrt{c o s (x)}}$

Question Number 124579 Answers: 5 Comments: 0

I=∫_0 ^( ∞) (dx/((x+(√(x^2 +1)))^2 )) ?

$I = \int_{0}^{\infty} \frac{d x}{{(x + \sqrt{x^{2} + 1})}^{2}} ?$

Question Number 124566 Answers: 4 Comments: 0

∫ (dx/((x+(√(x^2 +1)))^2 ))

$\int \frac{d x}{{(x + \sqrt{x^{2} + 1})}^{2}}$

Question Number 124542 Answers: 1 Comments: 1

help ∫3xdx

$h e l p \int 3 x d x$

Question Number 124540 Answers: 2 Comments: 0

∫((4x+9)/(x^2 +6x+10))dx

$\int \frac{4 x + 9}{x^{2} + 6 x + 10} d x$

Question Number 124532 Answers: 5 Comments: 0

∫ (dx/(x^2 (√(x^2 −1)))) ?

$\int \frac{d x}{x^{2} \sqrt{x^{2} - 1}} ?$

Question Number 124531 Answers: 1 Comments: 0

calculate ∫_0 ^∞ (dx/((2x+1)^4 (x+3)^5 ))

$c a l c u l a t e \int_{0}^{\infty} \frac{d x}{{(2 x + 1)}^{4} {(x + 3)}^{5}}$

Question Number 124530 Answers: 1 Comments: 1

find ∫_0 ^∞ cos(x^n )dx snd ∫_0 ^∞ sin(x^n )dx

$f i n d \int_{0}^{\infty} c o s (x^{n}) d x s n d \int_{0}^{\infty} s i n (x^{n}) d x$

Question Number 124482 Answers: 0 Comments: 0

∫e^(sinx) (((xcos^2 x−sinx)/(cos^2 x)))dx

$\int e^{sinx} (\frac{{xcos}^{2} x - sinx}{\cos^{2} x}) dx$

Question Number 124452 Answers: 1 Comments: 1

2 ((2x+1))^(1/3) = x^3 −1

$2 \sqrt[3]{2 x + 1} = x^{3} - 1$

Question Number 124438 Answers: 1 Comments: 2

∫e^((xsinx+cosx)) ∙(((x^4 cos^3 x−xsinx+cosx)/(x^2 cos^2 x)))dx

$\int e^{(xsinx + cosx)} \cdot (\frac{x^{4} \cos^{3} x - xsinx + cosx}{x^{2} \cos^{2} x}) dx$

Question Number 124432 Answers: 3 Comments: 0

... nice calculus... find:: φ=∫_0 ^( 4) ((ln(x))/((4x−x^2 )^(1/2) ))dx=?

$. . . n i c e c a l c u l u s . . .$ $f i n d ::$ $ϕ = \int_{0}^{4} \frac{l n (x)}{{(4 x - x^{2})}^{\frac{1}{2}}} d x = ?$

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