Question and Answers Forum

let f(a)=∫_0 ^1 (dt/((√(x+a)) +3)) 1) calculate f(a) 2) find also ∫_0 ^1 (dt/((√(x+a))((√(x+a)) +3)^2 )) 3) find the values of integrals ∫_0 ^1 (dt/((√(x+1))+3)) and ∫_0 ^1 (dt/((√(x+1))((√(x+1))+3)^2 ))

$l e t f (a) = \int_{0}^{1} \frac{d t}{\sqrt{x + a} + 3}$ $1) c a l c u l a t e f (a)$ $2) f i n d a l s o \int_{0}^{1} \frac{d t}{\sqrt{x + a} {(\sqrt{x + a} + 3)}^{2}}$ $3) f i n d t h e v a l u e s o f i n t e g r a l s \int_{0}^{1} \frac{d t}{\sqrt{x + 1} + 3} a n d \int_{0}^{1} \frac{d t}{\sqrt{x + 1} {(\sqrt{x + 1} + 3)}^{2}}$

Question Number 53476 Answers: 0 Comments: 0

let f(x)=∫_0 ^x t(√(2t−1))dt calculate ∣sup_(1≤x≤2) f(x) −inf_(1≤x≤2) f(x)∣

$l e t f (x) = \int_{0}^{x} t \sqrt{2 t - 1} d t c a l c u l a t e ∣ {s u p}_{1 ⩽ x ⩽ 2} f (x) - {i n f}_{1 ⩽ x ⩽ 2} f (x) ∣$

Question Number 53474 Answers: 1 Comments: 0

calculate ∫_0 ^1 ((5^(2x+1) −2^(2x−1) )/(10^x )) dx

$c a l c u l a t e \int_{0}^{1} \frac{5^{2 x + 1} - 2^{2 x - 1}}{10^{x}} d x$

Question Number 53471 Answers: 1 Comments: 3

1)find U_n = ∫_0 ^(π/4) tan^n tdt with n integr . 2) find lim_(n→+∞) U_n 3) calculate Σ_(n=0) ^∞ U_n

$1) f i n d U_{n} = \int_{0}^{\frac{π}{4}} {t a n}^{n} t d t w i t h n i n t e g r .$ $2) f i n d {l i m}_{n \to + \infty} U_{n}$ $3) c a l c u l a t e \sum_{n = 0}^{\infty} U_{n}$

Question Number 53470 Answers: 0 Comments: 1

find Vn=∫_(1/n) ^((an−1)/n) ((√x)/(√(a−(√x)+x)))dx

$f i n d V n = \int_{\frac{1}{n}}^{\frac{a n - 1}{n}} \frac{\sqrt{x}}{\sqrt{a - \sqrt{x} + x}} d x$

Question Number 53467 Answers: 1 Comments: 0

let A_(n m) =∫_0 ^1 x^n (1−x)^m dx with n and n integrs naturals 1) calculate A_(n m) by using factoriels 2) find Σ_(n,m) A_(nm)

$l e t A_{n m} = \int_{0}^{1} x^{n} {(1 - x)}^{m} d x w i t h n a n d n i n t e g r s n a t u r a l s$ $1) c a l c u l a t e A_{n m} b y u s i n g f a c t o r i e l s$ $2) f i n d \sum_{n, m} A_{n m}$

Question Number 53465 Answers: 1 Comments: 1

find ∫_(−(π/2)) ^(π/2) (√(cosx −cos^3 x))dx

$f i n d \int_{- \frac{π}{2}}^{\frac{π}{2}} \sqrt{c o s x - {c o s}^{3} x} d x$

Question Number 53464 Answers: 1 Comments: 1

let U_n = (((∫_0 ^n e^(−x^2 ) dx)^2 )/(∫_0 ^n e^(−nx^2 ) dx)) 1) calculate lim_(n→+∞) U_n 2) determne nature of Σ U_n and Σ U_n ^3 .

$l e t U_{n} = \frac{{(\int_{0}^{n} e^{- x^{2}} d x)}^{2}}{\int_{0}^{n} e^{- {n x}^{2}} d x}$ $1) c a l c u l a t e {l i m}_{n \to + \infty} U_{n}$ $2) d e t e r m n e n a t u r e o f Σ U_{n} a n d Σ U_{n}^{3} .$

Question Number 53463 Answers: 1 Comments: 1

1)let 0<θ<(π/2) and A(θ) =∫_0 ^(π/2) (dx/(√(x^2 +2sinθ x +1))) calculate A(θ) 2) calculate ∫_0 ^(π/2) (dx/(√(x^2 +(√2)x +1)))

$1) l e t 0 < θ < \frac{π}{2} a n d A (θ) = \int_{0}^{\frac{π}{2}} \frac{d x}{\sqrt{x^{2} + 2 s i n θ x + 1}}$ $c a l c u l a t e A (θ)$ $2) c a l c u l a t e \int_{0}^{\frac{π}{2}} \frac{d x}{\sqrt{x^{2} + \sqrt{2} x + 1}}$

Question Number 53462 Answers: 1 Comments: 0

find ∫_(−(π/4)) ^(π/4) ((xsinx)/(cos^2 x))dx

$f i n d \int_{- \frac{π}{4}}^{\frac{π}{4}} \frac{x s i n x}{{c o s}^{2} x} d x$

Question Number 53536 Answers: 1 Comments: 0

If [x] stands for the gratest integer function the value of ∫_4 ^(10) (([x^2 ])/([x^2 −28x+196]+[x^2 ])) dx is

$If [x] stands for the gratest integer function$ $the value of \int_{4}^{10} \frac{[x^{2}]}{[x^{2} - 28 x + 196] + [x^{2}]} d x is$

Question Number 53418 Answers: 0 Comments: 1

find ∫_0 ^π (x/(2+cosx sinx))dx

$f i n d \int_{0}^{π} \frac{x}{2 + c o s x s i n x} d x$

Question Number 53378 Answers: 1 Comments: 0

if u=e^(xyz) then u_(xyx) =? a)u((xyz)^2 +3xyz+1) b)u(3(xyz)^2 +1) c)u((xyz)^2 +2yz+1) please help

$i f u = e^{x y z} t h e n u_{x y x} = ?$ $a) u ({(x y z)}^{2} + 3 x y z + 1) b) u (3 {(x y z)}^{2} + 1)$ $c) u ({(x y z)}^{2} + 2 y z + 1)$ $p l e a s e h e l p$

Question Number 53295 Answers: 1 Comments: 1

∫_0 ^(π/2) (1/(2+cos x)) dx=...

$\int_{0}^{\frac{π}{2}} \frac{1}{2 + \cos x} d x = . . .$

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