Question and Answers Forum

let W(x) =∫_(−∞) ^(+∞) ((arctan(xt^2 ))/(2+t^2 ))dt 1) find a explicit form of f(x) 2) find the value of ∫_(−∞) ^(+∞) (t^2 /((2+t^2 )(1+x^2 t^4 )))dt .

$l e t W (x) = \int_{- \infty}^{+ \infty} \frac{a r c t a n ({x t}^{2})}{2 + t^{2}} d t$ $1) f i n d a e x p l i c i t f o r m o f f (x)$ $2) f i n d t h e v a l u e o f \int_{- \infty}^{+ \infty} \frac{t^{2}}{(2 + t^{2}) (1 + x^{2} t^{4})} d t .$

Question Number 48062 Answers: 0 Comments: 0

calculate ∫_(−∞) ^(+∞) (((x^2 −3)sin(2x^2 ))/((x^2 +1)^3 ))dx

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

Question Number 48057 Answers: 2 Comments: 1

Question Number 48043 Answers: 0 Comments: 1

let f(α) =∫_(−∞) ^(+∞) ((cos(αx^3 ))/(x^2 +8)) dx 1)calculate f(α) 2) calculate ∫_(−∞) ^(+∞) ((cos(2x^3 ))/(x^2 +8))dx .

$l e t f (α) = \int_{- \infty}^{+ \infty} \frac{c o s (α x^{3})}{x^{2} + 8} d x$ $1) c a l c u l a t e f (α)$ $2) c a l c u l a t e \int_{- \infty}^{+ \infty} \frac{c o s (2 x^{3})}{x^{2} + 8} d x .$

Question Number 48042 Answers: 0 Comments: 1

find the value of ∫_(−∞) ^(+∞) ((2x+1)/((x^2 +i)(x^2 +4)))dx (i^2 =−1)

$f i n d t h e v a l u e o f \int_{- \infty}^{+ \infty} \frac{2 x + 1}{(x^{2} + i) (x^{2} + 4)} d x (i^{2} = - 1)$

Question Number 48040 Answers: 0 Comments: 1

let f(α)=∫_(−∞) ^(+∞) ((xsin(αx))/((1+x^2 )^2 ))dx calculate f(α) and f^′ (α).(α from R) .

$l e t f (α) = \int_{- \infty}^{+ \infty} \frac{x s i n (α x)}{{(1 + x^{2})}^{2}} d x$ $c a l c u l a t e f (α) a n d f^{^{'}} (α) . (α f r o m R) .$

Question Number 48027 Answers: 2 Comments: 1

Question Number 47985 Answers: 1 Comments: 3

calculate I=∫_0 ^1 (√(1+2(√(x−x^2 ))))dx and J =∫_0 ^1 (√(1−2(√(x−x^2 ))))dx

$c a l c u l a t e I = \int_{0}^{1} \sqrt{1 + 2 \sqrt{x - x^{2}}} d x a n d J = \int_{0}^{1} \sqrt{1 - 2 \sqrt{x - x^{2}}} d x$

Question Number 47967 Answers: 1 Comments: 0

A particle moves in a linear scare such that acceleration after t seconds is a ms^(−2) where a= 2t^2 + t.If its initial velocity was 3ms^(−1) find an expression for S,the distance in meters traveled from start t seconds.

$A p a r t i c l e m o v e s i n a l i n e a r s c a r e s u c h t h a t a c c e l e r a t i o n$ $a f t e r t s e c o n d s i s a {m s}^{- 2} w h e r e a = 2 t^{2} + t . I f i t s i n i t i a l$ $v e l o c i t y w a s 3 {m s}^{- 1} f i n d a n e x p r e s s i o n f o r S, t h e d i s t a n c e i n m e t e r s$ $t r a v e l e d f r o m s t a r t t s e c o n d s .$

Question Number 47915 Answers: 2 Comments: 0

Question Number 47863 Answers: 0 Comments: 0

find ∫ (√(1−x^4 ))dx

$f i n d \int \sqrt{1 - x^{4}} d x$

Question Number 47852 Answers: 0 Comments: 1

1) find ∫ x arctan(x)dx 2) find the value of ∫_0 ^1 x arctan(x)dx

$1) f i n d \int x a r c t a n (x) d x$ $2) f i n d t h e v a l u e o f \int_{0}^{1} x a r c t a n (x) d x$

Question Number 47851 Answers: 2 Comments: 3

let f(x)=x+1+(√x) and g(x)=x+1−(√x) find ∫ ((f(x))/(g(x)))dx and ((∫f(x)dx)/(∫g(x)dx)) .

$l e t f (x) = x + 1 + \sqrt{x} a n d g (x) = x + 1 - \sqrt{x}$ $f i n d \int \frac{f (x)}{g (x)} d x a n d \frac{\int f (x) d x}{\int g (x) d x} .$

Question Number 47850 Answers: 1 Comments: 2

calculate A_p =∫_0 ^1 ((x^p −1)/(ln(x)))dx with p>0.

$c a l c u l a t e A_{p} = \int_{0}^{1} \frac{x^{p} - 1}{l n (x)} d x w i t h p > 0 .$

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