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AllQuestion and Answers: Page 1643

Question Number 38478 Answers: 0 Comments: 1

Question Number 38477 Answers: 1 Comments: 0

Question Number 38475 Answers: 1 Comments: 0

A committee of 2 girls and 3boys is to be form from 6girls and 8boys how many different committee can be formed ?

$A c o m m i t t e e o f 2 g i r l s a n d 3 b o y s$ $i s t o b e f o r m f r o m 6 g i r l s a n d 8 b o y s$ $h o w m a n y d i f f e r e n t c o m m i t t e e c a n$ $b e f o r m e d$ $?$

Question Number 38470 Answers: 0 Comments: 4

calculate f(t)=∫_0 ^∞ ((cos(tx))/((1+tx^2 )^2 )) dx with t≥0 2) find the values of ∫_0 ^∞ ((cos(2x))/((1+2x^2 )^2 ))dx and ∫_0 ^∞ ((cosx)/((2+x^2 )^2 ))dx

$c a l c u l a t e f (t) = \int_{0}^{\infty} \frac{c o s (t x)}{{(1 + {t x}^{2})}^{2}} d x w i t h t ⩾ 0$ $2) f i n d t h e v a l u e s o f \int_{0}^{\infty} \frac{c o s (2 x)}{{(1 + 2 x^{2})}^{2}} d x a n d \int_{0}^{\infty} \frac{c o s x}{{(2 + x^{2})}^{2}} d x$

Question Number 38469 Answers: 0 Comments: 1

calculate f(a) = ∫_(−∞) ^(+∞) ((sin(ax))/(x^2 +x+1))dx 2) find the value of ∫_(−∞) ^(+∞) ((sin(3x))/(x^2 +x+1))dx

$c a l c u l a t e f (a) = \int_{- \infty}^{+ \infty} \frac{s i n (a x)}{x^{2} + x + 1} d x$ $2) f i n d t h e v a l u e o f \int_{- \infty}^{+ \infty} \frac{s i n (3 x)}{x^{2} + x + 1} d x$

Question Number 38468 Answers: 0 Comments: 1

calculate ∫_(−∞) ^(+∞) ((sin(2x)sh(3x))/(4+x^2 ))dx

$c a l c u l a t e \int_{- \infty}^{+ \infty} \frac{s i n (2 x) s h (3 x)}{4 + x^{2}} d x$

Question Number 38467 Answers: 0 Comments: 1

calculate ∫_(−∞) ^(+∞) ((cos(ax)ch(bx))/(x^2 +1))dx .

$c a l c u l a t e \int_{- \infty}^{+ \infty} \frac{c o s (a x) c h (b x)}{x^{2} + 1} d x .$

Question Number 38466 Answers: 0 Comments: 1

let a from R find F_a (t)= ∫_(−∞) ^(+∞) ((cos(tx))/(a^2 +x^2 ))dx 2) calculate F_2 (3) and F_3 (2)

$l e t a f r o m R f i n d F_{a} (t) = \int_{- \infty}^{+ \infty} \frac{c o s (t x)}{a^{2} + x^{2}} d x$ $2) c a l c u l a t e F_{2} (3) a n d F_{3} (2)$

Question Number 38465 Answers: 0 Comments: 2

find f(x)= ∫_0 ^1 ln(1+xt^3 )dt with ∣x∣<1 . 2) calculate ∫_0 ^1 ln(1+4t^3 )dt and ∫_0 ^1 ln(2+t^3 )dt.

$f i n d f (x) = \int_{0}^{1} l n (1 + {x t}^{3}) d t w i t h ∣ x ∣< 1 .$ $2) c a l c u l a t e \int_{0}^{1} l n (1 + 4 t^{3}) d t a n d \int_{0}^{1} l n (2 + t^{3}) d t .$

Question Number 38464 Answers: 0 Comments: 1

let f(x)= ∫_0 ^1 ((ln(1−x^2 t^2 ))/t^2 )dt with ∣x∣<1 find f(x) at a simple form .

$l e t f (x) = \int_{0}^{1} \frac{l n (1 - x^{2} t^{2})}{t^{2}} d t w i t h ∣ x ∣< 1$ $f i n d f (x) a t a s i m p l e f o r m .$

Question Number 38463 Answers: 0 Comments: 1

calculate I = ∫_0 ^1 ((ln (1−(t^2 /4)))/t^2 )dt

$c a l c u l a t e I = \int_{0}^{1} \frac{l n (1 - \frac{t^{2}}{4})}{t^{2}} d t$

Question Number 38462 Answers: 0 Comments: 0

find ∫_1 ^(+∞) arctan(x −(1/x))dx

$f i n d \int_{1}^{+ \infty} a r c t a n (x - \frac{1}{x}) d x$

Question Number 38461 Answers: 0 Comments: 0

find f(x) = ∫_0 ^∞ arctan(1+e^(−xt) )dt with x>0 2) find ∫_0 ^∞ arctan(1+e^(−2t) )dt.

$f i n d f (x) = \int_{0}^{\infty} a r c t a n (1 + e^{- x t}) d t w i t h x > 0$ $2) f i n d \int_{0}^{\infty} a r c t a n (1 + e^{- 2 t}) d t .$

Question Number 38453 Answers: 0 Comments: 4

find f(x)=∫_0 ^∞ ((1−cos(xt))/t) e^(−xt) dt with x>0 1) find asimple form of f(x) 2) calculate ∫_0 ^∞ ((1−cos(πt))/t) e^(−t) dt 3)calculate ∫_0 ^∞ ((1−cos(3t))/t) e^(−2t) dt

$f i n d f (x) = \int_{0}^{\infty} \frac{1 - c o s (x t)}{t} e^{- x t} d t w i t h x > 0$ $1) f i n d a s i m p l e f o r m o f f (x)$ $2) c a l c u l a t e \int_{0}^{\infty} \frac{1 - c o s (π t)}{t} e^{- t} d t$ $3) c a l c u l a t e \int_{0}^{\infty} \frac{1 - c o s (3 t)}{t} e^{- 2 t} d t$

Question Number 39416 Answers: 1 Comments: 0

Given that f(x) is a cubic function and f(x) = x^3 − (x^2 /4) + 5x − 7 a) find one factor of f(x) b) find (d^2 y/dx^2 ) for f(x) c) hence Evaluate y = ∫_0 ^∞ f(x).

$G i v e n t h a t f (x) i s a c u b i c f u n c t i o n$ $a n d f (x) = x^{3} - \frac{x^{2}}{4} + 5 x - 7$ $a) f i n d o n e f a c t o r o f f (x)$ $b) f i n d \frac{d^{2} y}{{d x}^{2}} f o r f (x)$ $c) h e n c e E v a l u a t e y = \int_{0}^{\infty} f (x) .$

Question Number 38451 Answers: 1 Comments: 1

new attempt to solve qu. 37630 ∫(dx/((√x)+(√(x+1))+(√(x+2))))= [t=x+1 → dx=dt] =∫(dt/((√(t−1))+(√t)+(√(t+1))))= [((to omit the roots)),(((√a)+(√b)+(√c) must be multiplied with)),(((−(√a)−(√b)+(√c))(−(√a)+(√b)−(√c))((√a)−(√b)−(√c)))),(((1/((√a)+(√b)+(√c)))=((a^(3/2) +b^(3/2) +c^(3/2) +2(√(abc))−((a+b)(√c)+(a+c)(√b)+(b+c)(√a)))/(a^2 +b^2 +c^2 −2(ab+ac+bc))))) ] =∫((t(√(t−1))+t(√t)+t(√(t+1))+2(√(t−1))−2(√(t+1))−2(√((t−1)t(t+1))))/(3t^2 −4))dt= =∫((t(√(t−1)))/(3t^2 −4))dt+∫((t(√t))/(3t^2 −4))dt+∫((t(√(t+1)))/(3t^2 −4))dt+2∫((√(t−1))/(3t^2 −4))dt−2∫((√(t+1))/(3t^2 −4))−2∫((√((t−1)t(t+1)))/(3t^2 −4))dt I think I can solve them all except the last one so please somebody try ∫((√((t−1)t(t+1)))/(3t^2 −4))dt=? I will do the others tomorrow

$new attempt to solve qu . 37630$ $\int \frac{d x}{\sqrt{x} + \sqrt{x + 1} + \sqrt{x + 2}} =$ $[t = x + 1 \to d x = d t]$ $= \int \frac{d t}{\sqrt{t - 1} + \sqrt{t} + \sqrt{t + 1}} =$ $[\begin{matrix} to omit the roots \\ \sqrt{a} + \sqrt{b} + \sqrt{c} must be multiplied with \\ (- \sqrt{a} - \sqrt{b} + \sqrt{c}) (- \sqrt{a} + \sqrt{b} - \sqrt{c}) (\sqrt{a} - \sqrt{b} - \sqrt{c}) \\ \frac{1}{\sqrt{a} + \sqrt{b} + \sqrt{c}} = \frac{a^{3 / 2} + b^{3 / 2} + c^{3 / 2} + 2 \sqrt{a b c} - ((a + b) \sqrt{c} + (a + c) \sqrt{b} + (b + c) \sqrt{a})}{a^{2} + b^{2} + c^{2} - 2 (a b + a c + b c)} \end{matrix}]$ $= \int \frac{t \sqrt{t - 1} + t \sqrt{t} + t \sqrt{t + 1} + 2 \sqrt{t - 1} - 2 \sqrt{t + 1} - 2 \sqrt{(t - 1) t (t + 1)}}{3 t^{2} - 4} d t =$ $= \int \frac{t \sqrt{t - 1}}{3 t^{2} - 4} d t + \int \frac{t \sqrt{t}}{3 t^{2} - 4} d t + \int \frac{t \sqrt{t + 1}}{3 t^{2} - 4} d t + 2 \int \frac{\sqrt{t - 1}}{3 t^{2} - 4} d t - 2 \int \frac{\sqrt{t + 1}}{3 t^{2} - 4} - 2 \int \frac{\sqrt{(t - 1) t (t + 1)}}{3 t^{2} - 4} d t$ $I think I can solve them all except the last one$ $so please somebody try$ $\int \frac{\sqrt{(t - 1) t (t + 1)}}{3 t^{2} - 4} d t = ?$ $I will do the others tomorrow$

Question Number 38460 Answers: 0 Comments: 1

let ∣x∣>1 find the value of F(x)=∫_0 ^∞ ln(1+xt^2 )dt 2)calculate ∫_0 ^∞ ln(1+3t^2 )dt .

$l e t ∣ x ∣> 1 f i n d t h e v a l u e o f$ $F (x) = \int_{0}^{\infty} l n (1 + {x t}^{2}) d t$ $2) c a l c u l a t e \int_{0}^{\infty} l n (1 + 3 t^{2}) d t .$

Question Number 38459 Answers: 0 Comments: 7

x^2 (x−b^2 )+a^2 b^2 (x−a^2 )=0 Solve for x.

$x^{2} (x - b^{2}) + a^{2} b^{2} (x - a^{2}) = 0$ $S o l v e f o r x .$

Question Number 38458 Answers: 0 Comments: 3

let ∣x∣<1 calculate F(x)=∫_0 ^1 ln(1+xt^2 )dt 2) find the value of ∫_0 ^1 ln(1 +(1/2)t^2 )dt 3)find the value of A(θ) =∫_0 ^1 ln(1+sinθ t^2 )dt .

$l e t ∣ x ∣< 1 c a l c u l a t e F (x) = \int_{0}^{1} l n (1 + {x t}^{2}) d t$ $2) f i n d t h e v a l u e o f \int_{0}^{1} l n (1 + \frac{1}{2} t^{2}) d t$ $3) f i n d t h e v a l u e o f A (θ) = \int_{0}^{1} l n (1 + s i n θ t^{2}) d t .$

Question Number 38457 Answers: 0 Comments: 0

f is a C^2 function prove that 1)L(f^′ )=x L(f)−f(0^+ ) 2)L(f^(′′) )=x^2 L(f) −xf(0^+ )−f^′ (0^+ ) L means Laplace transform.

$f i s a C^{2} f u n c t i o n p r o v e t h a t$ $1) L (f^{^{'}}) = x L (f) - f (0^{+})$ $2) L (f^{^{″}}) = x^{2} L (f) - x f (0^{+}) - f^{^{'}} (0^{+})$ $L m e a n s L a p l a c e t r a n s f o r m .$

Question Number 38456 Answers: 0 Comments: 0

calculate Σ_(n=1) ^∞ (−1)^n ((cos(nx))/n^2 ) and Σ_(n=1) ^∞ (−1)^n ((sin(nx))/n^2 )

$c a l c u l a t e \sum_{n = 1}^{\infty} {(- 1)}^{n} \frac{c o s (n x)}{n^{2}} a n d \sum_{n = 1}^{\infty} {(- 1)}^{n} \frac{s i n (n x)}{n^{2}}$

Question Number 38455 Answers: 0 Comments: 0

solve the d.e y^′ −xe^(−2x) y =cos(3x)

$s o l v e t h e d . e y^{^{'}} - {x e}^{- 2 x} y = c o s (3 x)$

Question Number 38454 Answers: 0 Comments: 3

let f(x)=∫_0 ^∞ ((1−cos(xt^2 ))/t^2 ) e^(−xt^2 ) dt with x>0 1) find a simple form of f(x) 2) calculate ∫_0 ^∞ ((1−cos(2t^2 ))/t^2 ) e^(−3t^2 ) dt .

$l e t f (x) = \int_{0}^{\infty} \frac{1 - c o s ({x t}^{2})}{t^{2}} e^{- {x t}^{2}} d t w i t h x > 0$ $1) f i n d a s i m p l e f o r m o f f (x)$ $2) c a l c u l a t e \int_{0}^{\infty} \frac{1 - c o s (2 t^{2})}{t^{2}} e^{- 3 t^{2}} d t .$

Question Number 38405 Answers: 1 Comments: 2

If f(3)=3;f(1)=2 ⇒∫_1 ^3 f(x)f^′ (x)dx=.....

$If f (3) = 3; f (1) = 2$ $\Rightarrow \int_{1}^{3} f (x) f^{^{'}} (x) dx = . . . . .$

Question Number 38397 Answers: 2 Comments: 2

evaluate ∫secxdx

$e v a l u a t e \int s e c x d x$

Question Number 38395 Answers: 1 Comments: 1

Find roots of the equation z^2 +2(1+i)z +2=0 leaving your answer in a+ib

$F i n d r o o t s o f t h e e q u a t i o n$ $z^{2} + 2 (1 + i) z + 2 = 0$ $l e a v i n g y o u r a n s w e r i n a + i b$

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