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IntegrationQuestion and Answers: Page 193

Question Number 82244 Answers: 1 Comments: 2

find the function of f when this function continue at interval [−∞,0] ∫_(−x^2 ) ^0 f(t) dt=(d/dx)[x(1−sin(πx)]

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

Question Number 82232 Answers: 1 Comments: 1

Question Number 82223 Answers: 0 Comments: 1

given f(x) = f(x+(π/6)) , ∀x∈ R if ∫_0 ^(π/6) f(x) dx = T then ∫_π ^((7π)/3) f(x+π) dx = ?

$g i v e n f (x) = f (x + \frac{π}{6}), \forall x \in R$ $i f \underset{0}{\int^{\frac{π}{6}}} f (x) d x = T$ $t h e n \underset{π}{\int^{\frac{7 π}{3}}} f (x + π) d x = ?$

Question Number 82185 Answers: 1 Comments: 2

∫ (dx/(sec x + csc x)) = ?

$\int \frac{d x}{\sec x + c s c x} = ?$

Question Number 82174 Answers: 1 Comments: 1

∫_0 ^π x ln(sin x) dx = ?

$\underset{0}{\int^{π}} x l n (\sin x) d x = ?$

Question Number 82139 Answers: 1 Comments: 0

∫ ((√(x^4 +x^(−4) +2))/x^3 ) dx

$\int \frac{\sqrt{x^{4} + x^{- 4} + 2}}{x^{3}} d x$

Question Number 82022 Answers: 0 Comments: 0

Question Number 82020 Answers: 0 Comments: 2

Question Number 81996 Answers: 0 Comments: 0

calculate I_n =∫∫_([(1/n),n[) e^(−x^2 −3y^2 ) dxdy and find lim_(n→+∞) I_n conclude that ∫_0 ^∞ e^(−x^2 ) dx=((√π)/2)

$c a l c u l a t e I_{n} = \int \int_{[\frac{1}{n}, n [} e^{- x^{2} - 3 y^{2}} d x d y$ $a n d f i n d {l i m}_{n \to + \infty} I_{n}$ $c o n c l u d e t h a t \int_{0}^{\infty} e^{- x^{2}} d x = \frac{\sqrt{π}}{2}$

Question Number 81994 Answers: 0 Comments: 0

calculate ∫∫_W (x+y)e^(x−y) dxdy with W is the triangle limited by o,A(1,0)and B(0,1)

$c a l c u l a t e \int \int_{W} (x + y) e^{x - y} d x d y$ $w i t h W i s t h e t r i a n g l e l i m i t e d b y$ $o, A (1, 0) a n d B (0, 1)$

Question Number 81993 Answers: 0 Comments: 0

calculate ∫∫_D ln(1+x+y)dxdy with D is the triangle limited by points 0,A(1,0) and B(0,1)

$c a l c u l a t e \int \int_{D} l n (1 + x + y) d x d y$ $w i t h D i s t h e t r i a n g l e l i m i t e d b y$ $p o i n t s 0, A (1, 0) a n d B (0, 1)$

Question Number 81921 Answers: 1 Comments: 0

Question Number 81889 Answers: 1 Comments: 0

Question Number 81888 Answers: 1 Comments: 1

Question Number 81801 Answers: 1 Comments: 1

Question Number 81739 Answers: 2 Comments: 1

∫(dx/(cos^3 x−sin^3 x))

$\int \frac{d x}{{c o s}^{3} x - {s i n}^{3} x}$

Question Number 81719 Answers: 0 Comments: 1

1) find ∫ (dx/((x+2)^5 (x−3)^9 )) 2) calculate ∫_4 ^(+∞) (dx/((x+2)^5 (x−3)^9 ))

$1) f i n d \int \frac{d x}{{(x + 2)}^{5} {(x - 3)}^{9}}$ $2) c a l c u l a t e \int_{4}^{+ \infty} \frac{d x}{{(x + 2)}^{5} {(x - 3)}^{9}}$

Question Number 81636 Answers: 0 Comments: 4

∫ ((x(tan^(−1) (x))^2 )/((1+x^2 )^(3/2) )) dx =

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

Question Number 81591 Answers: 0 Comments: 6

if g(−2)=−5 and g′(x)= (x^2 /(cos^2 (x)+1)) find g(4)

$if g (- 2) = - 5 and$ $g^{'} (x) = \frac{x^{2}}{\cos^{2} (x) + 1}$ $find g (4)$

Question Number 81549 Answers: 0 Comments: 5

∫_0 ^4 ⌊x⌋^2 dx = ∫_0 ^4 ⌊x^2 ⌋dx=

$\underset{0}{\int^{4}} ⌊ x ⌋^{2} dx =$ $\underset{0}{\int^{4}} ⌊ x^{2} ⌋ dx =$

Question Number 81482 Answers: 1 Comments: 1

Evaluate ∫_(−∞) ^∞ (dx/(x^2 +4x+13)).

$E v a l u a t e \int_{- \infty}^{\infty} \frac{d x}{x^{2} + 4 x + 13} .$

Question Number 81433 Answers: 1 Comments: 0

calculate ∫_2 ^(+∞) ((2x+3)/((x−1)^3 (x^2 +x+1)^2 ))dx

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

Question Number 81432 Answers: 1 Comments: 1

find ∫ (dx/((x+1)^3 (x^2 +3)^2 ))

$f i n d \int \frac{d x}{{(x + 1)}^{3} {(x^{2} + 3)}^{2}}$

Question Number 81427 Answers: 1 Comments: 4

1) calculate ∫_0 ^∞ cos(x^3 )dx 2)find the value of ∫_0 ^∞ cos(x^n )dx with n≥2

$1) c a l c u l a t e \int_{0}^{\infty} c o s (x^{3}) d x$ $2) f i n d t h e v a l u e o f \int_{0}^{\infty} c o s (x^{n}) d x w i t h n ⩾ 2$

Question Number 81400 Answers: 1 Comments: 3

Hello Nice day im thinking of this one a close forme? ∫(√(1+x^p ))dx p∈R_+ , x∈[0,1[

$H e l l o N i c e d a y i m t h i n k i n g o f t h i s o n e a c l o s e f o r m e ?$ $\int \sqrt{1 + x^{p}} d x$ $p \in R_{+},$ $x \in [0, 1 [$

Question Number 81340 Answers: 1 Comments: 4

Quation posted Times ago i can′t find it .after Somme Try i got close Fofme ∫_0 ^π sin(x^2 )dx=(π^3 /3) _1 F_2 ((3/4);(3/2);(7/4),−(π^4 /4))? sin(x)=Σ_(k≥0) (((−1)^k x^(2k+1) )/((2k+1)!)) ⇒sin(x^2 )=Σ_(k≥0) (((−1)^k x^(4k+2) )/((2k+1)!)) ∫_0 ^π sin(x^2 )dx=Σ_(k≥0) (((−1)^k )/((2k+1)!))∫_0 ^π x^(4k+2) dx =Σ_(k≥0) (((−1)^k π^(4k+3) )/((2k+1)!(4k+3))) =(π^3 /3)Σ_(k≥0) ((3(−1)^k π^(4k) )/((2k+1)!(4k+3))) (2k+1)!=k!.Π_(j=1) ^(k+1) (k+j)=k!.2^k .3....(2k+1) =(π^3 /3).Σ_(k≥0) ((3(−1)^k π^(4k) )/(k!.2^k .3....(2k+1)(4k+3))) =(π^3 /3)Σ_(k≥0) ((2^k .3)/(3...(2k+1).(4k+3))).(((−π^4 )/4))^k .(1/(k!)) =(π^3 /3).Σ_(k≥0) ((2^k .3.....(4k−1))/(3.....(2k+1).(7.....(4k−1)(4k+3))).(((−π^4 )/4))^k .(1/(k!)) =(π^3 /3).Σ_(k≥0) (((1/4^k ).(3)...(4k−1))/((1/2^k ).(3)...(2k+1).(1/4^k )(7)...(4k+3))).(−(π^4 /4))^k .(1/(k!)) =(π^3 /3)Σ_(k≥0) ((((3/4))....((3/4)+k−1))/(((3/2))....((3/2)+k−1).((7/4))....((7/4)+k−1))).(((−π^4 )/4))^k .(1/(k!)) =(π^3 /3) _1 F_2 ((3/4);(3/2);(7/4);−(π^4 /4))

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