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IntegrationQuestion and Answers: Page 302

Question Number 32420 Answers: 0 Comments: 0

Question Number 32419 Answers: 0 Comments: 0

Question Number 32367 Answers: 0 Comments: 0

let α∈R and x^2 ≠1 find the value of f(x) = ∫_0 ^π ln(x^2 −2x cost +1)dt calculate f(x).

$l e t α \in R a n d x^{2} \neq 1 f i n d t h e v a l u e o f$ $f (x) = \int_{0}^{π} l n (x^{2} - 2 x c o s t + 1) d t$ $c a l c u l a t e f (x) .$

Question Number 32365 Answers: 0 Comments: 3

let F(x) = ∫_0 ^π ln(1+xcosθ)dθ .with ∣x∣<1 find F(x) .

$l e t F (x) = \int_{0}^{π} l n (1 + x c o s θ) d θ . w i t h ∣ x ∣< 1$ $f i n d F (x) .$

Question Number 32363 Answers: 0 Comments: 1

let consider the function f(x,θ) = ∫_x ^x^2 ln( 2+sinθ cost)dt calculate (∂f/∂x)(x,θ) and (∂f/∂θ)(x,θ) .

$l e t c o n s i d e r t h e f u n c t i o n$ $f (x, θ) = \int_{x}^{x^{2}} l n (2 + s i n θ c o s t) d t$ $c a l c u l a t e \frac{\partial f}{\partial x} (x, θ) a n d \frac{\partial f}{\partial θ} (x, θ) .$

Question Number 32362 Answers: 1 Comments: 0

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

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

Question Number 32361 Answers: 0 Comments: 1

let give a>0 find ∫_0 ^∞ (e^(−x) /(√(x+a))) dx.

$l e t g i v e a > 0 f i n d \int_{0}^{\infty} \frac{e^{- x}}{\sqrt{x + a}} d x .$

Question Number 32360 Answers: 0 Comments: 1

find the value of ∫_0 ^∞ (dx/((2x+1)(2x+3))) .

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

Question Number 32359 Answers: 0 Comments: 1

find ∫_0 ^∞ (dx/((1+x^2 )(1+x^4 ))) .

$f i n d \int_{0}^{\infty} \frac{d x}{(1 + x^{2}) (1 + x^{4})} .$

Question Number 32354 Answers: 0 Comments: 1

calculate ∫_0 ^(π/4) (dt/((1+sin^2 t)^2 )) .

$c a l c u l a t e \int_{0}^{\frac{π}{4}} \frac{d t}{{(1 + {s i n}^{2} t)}^{2}} .$

Question Number 32353 Answers: 1 Comments: 0

calculate ∫_0 ^(π/4) cos(x)ln(cos(x))dx .

$c a l c u l a t e \int_{0}^{\frac{π}{4}} c o s (x) l n (c o s (x)) d x .$

Question Number 32352 Answers: 1 Comments: 2

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

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

Question Number 32351 Answers: 1 Comments: 0

calculate ∫_0 ^(π/2) (dt/(1+cosθ sint)) .

$c a l c u l a t e \int_{0}^{\frac{π}{2}} \frac{d t}{1 + c o s θ s i n t} .$

Question Number 32350 Answers: 0 Comments: 0

calculate ∫_0 ^1 ^3 (√(x^2 (1−x))) dx

$c a l c u l a t e \int_{0}^{1}^{3} \sqrt{x^{2} (1 - x)} d x$

Question Number 32349 Answers: 0 Comments: 1

find the value of ∫_0 ^π ((xdx)/(1+sinx)) .

$f i n d t h e v a l u e o f \int_{0}^{π} \frac{x d x}{1 + s i n x} .$

Question Number 32343 Answers: 1 Comments: 1

calculate ∫_0 ^(2π) (dt/(x−e^(it) )) .

$c a l c u l a t e \int_{0}^{2 π} \frac{d t}{x - e^{i t}} .$

Question Number 32342 Answers: 0 Comments: 0

find the value of ∫∫_D ((dxdy)/((4x^2 +y^2 +1)^2 )) D={(x,y)∈ R^2 / x^2 +y^2 ≤1 and y ≤2x } .

$f i n d t h e v a l u e o f \int \int_{D} \frac{d x d y}{{(4 x^{2} + y^{2} + 1)}^{2}}$ $D = {(x, y) \in R^{2} / x^{2} + y^{2} ⩽ 1 a n d y ⩽ 2 x} .$

Question Number 32341 Answers: 0 Comments: 1

let give λ from R and λ^2 ≠1 and I_n (λ) = ∫_0 ^π ((cos(nt))/(1−2λcost +λ^2 ))dt .calculate I_n (λ).

$l e t g i v e λ f r o m R a n d λ^{2} \neq 1 a n d$ $I_{n} (λ) = \int_{0}^{π} \frac{c o s (n t)}{1 - 2 λ c o s t + λ^{2}} d t . c a l c u l a t e I_{n} (λ) .$

Question Number 32340 Answers: 0 Comments: 0

find the value of ∫_0 ^∞ ((sin^3 t)/t^2 ) dt .

$f i n d t h e v a l u e o f \int_{0}^{\infty} \frac{{s i n}^{3} t}{t^{2}} d t .$

Question Number 32339 Answers: 0 Comments: 1

calculate ∫_0 ^(+∞) ((th(3x) −th(2x))/x) dx .

$c a l c u l a t e \int_{0}^{+ \infty} \frac{t h (3 x) - t h (2 x)}{x} d x .$

Question Number 32338 Answers: 0 Comments: 0

find the value of ∫_0 ^1 ((ln(t))/((1+t)(√(1−t^2 )))) dt.

$f i n d t h e v a l u e o f \int_{0}^{1} \frac{l n (t)}{(1 + t) \sqrt{1 - t^{2}}} d t .$

Question Number 32337 Answers: 0 Comments: 0

1)calculate ∫_a ^(+∞) (dx/((1+x^2 )(√(x^2 −a^2 )))) with a>0 2) find the value of ∫_2 ^(+∞) (dx/((1+x^2 )(√(x^2 −4)))) .

$1) c a l c u l a t e \int_{a}^{+ \infty} \frac{d x}{(1 + x^{2}) \sqrt{x^{2} - a^{2}}} w i t h a > 0$ $2) f i n d t h e v a l u e o f \int_{2}^{+ \infty} \frac{d x}{(1 + x^{2}) \sqrt{x^{2} - 4}} .$

Question Number 32323 Answers: 1 Comments: 0

Given f(x) = (3/(16))(∫_0 ^1 f(x)dx)x^2 − (9/(10))(∫_0 ^2 f(x)dx)x + 2(∫_0 ^3 f(x)dx) + 4 Find f(x)

$Given$ $f (x) = \frac{3}{16} (\int_{0}^{1} f (x) d x) x^{2} - \frac{9}{10} (\int_{0}^{2} f (x) d x) x + 2 (\int_{0}^{3} f (x) d x) + 4$ $Find f (x)$

Question Number 32304 Answers: 0 Comments: 0

find lim_(x→+∞) e^(−x^2 ) ∫_0 ^x e^t^2 dt .

$f i n d {l i m}_{x \to + \infty} e^{- x^{2}} \int_{0}^{x} e^{t^{2}} d t .$

Question Number 32302 Answers: 1 Comments: 0

calculate ∫_1 ^2 (dx/(x +x(√x))) .

$c a l c u l a t e \int_{1}^{2} \frac{d x}{x + x \sqrt{x}} .$

Question Number 32301 Answers: 0 Comments: 1

calculate ∫_1 ^e ln(1+(√x))dx .

$c a l c u l a t e \int_{1}^{e} l n (1 + \sqrt{x}) d x .$

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