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IntegrationQuestion and Answers: Page 250

Question Number 49938 Answers: 0 Comments: 1

find f(x)=∫_0 ^(π/4) ln(cost+xsint)dt

$f i n d f (x) = \int_{0}^{\frac{π}{4}} l n (c o s t + x s i n t) d t$

Question Number 49922 Answers: 1 Comments: 0

Question Number 49902 Answers: 1 Comments: 1

If F(t)= ∫_0 ^( t) e^(t−y) .ydy. Prove that F(t)= e^t −(1+t).

$I f F (t) = \int_{0}^{t} e^{t - y} . y d y .$ $P r o v e t h a t F (t) = e^{t} - (1 + t) .$

Question Number 49903 Answers: 1 Comments: 1

Question Number 49898 Answers: 0 Comments: 1

Question Number 49838 Answers: 1 Comments: 1

∫(dx/(√((a+1)cos 2x +4cos x −a+3)))=?

$\int \frac{d x}{\sqrt{(a + 1) \cos 2 x + 4 \cos x - a + 3}} = ?$

Question Number 49829 Answers: 1 Comments: 1

∫(x^2 /(x^4 +1))dx

$\int \frac{x^{2}}{x^{4} + 1} d x$

Question Number 49827 Answers: 1 Comments: 4

The integral ∫_0 ^(1/2) ((ln (1+2x))/(1+4x^2 ))dx = ? a) (π/4)ln2 b)(π/8)ln2 c)(π/(16))ln2 d)(π/(32))ln2

$T h e i n t e g r a l \int_{0}^{\frac{1}{2}} \frac{\ln (1 + 2 x)}{1 + 4 x^{2}} d x = ?$ $a) \frac{π}{4} l n 2 b) \frac{π}{8} l n 2 c) \frac{π}{16} l n 2 d) \frac{π}{32} l n 2$

Question Number 49816 Answers: 2 Comments: 0

((sin^6 x−cos^6 x)/(sin^2 xcos^2 x)).intregrate

$\frac{\sin^{6} x - \cos^{6} x}{\sin^{2} {xcos}^{2} x} . intregrate$

Question Number 49815 Answers: 0 Comments: 3

sin^6 x−cos^6 x/sin^2 xcos^2 x

$\sin^{6} x - \cos^{6} x / \sin^{2} {xcos}^{2} x$

Question Number 49806 Answers: 0 Comments: 1

let f(x) =∫_0 ^(π/4) ln(1−x^2 cosθ)dθ with ∣x∣<1 1) find a explicit form of f(x) 2) calculate ∫_0 ^(π/4) ln(1−(1/4)cosθ)dθ .

$l e t f (x) = \int_{0}^{\frac{π}{4}} l n (1 - x^{2} c o s θ) d θ w i t h ∣ x ∣< 1$ $1) f i n d a e x p l i c i t f o r m o f f (x)$ $2) c a l c u l a t e \int_{0}^{\frac{π}{4}} l n (1 - \frac{1}{4} c o s θ) d θ .$

Question Number 49761 Answers: 1 Comments: 0

Calculate : ∫(( sin^2 x cos^2 x)/((sin^3 x+cos^3 x)^2 )) dx

$C a l c u l a t e :$ $\int \frac{\sin^{2} x \cos^{2} x}{{(\sin^{3} x + \cos^{3} x)}^{2}} d x$

Question Number 49760 Answers: 0 Comments: 3

Question Number 49746 Answers: 1 Comments: 0

∫((sin^8 x−cos^8 x)/(1−2sin^2 x.cos^2 x)) = ? a) ((−1)/2)sin 2x b)(1/2)sin 2x c)None.

$\int \frac{\sin^{8} x - \cos^{8} x}{1 - {2 \sin}^{2} x . \cos^{2} x} = ?$ $a) \frac{- 1}{2} \sin 2 x b) \frac{1}{2} \sin 2 x c) N o n e .$

Question Number 49708 Answers: 0 Comments: 0

Please integrate ∫(((e^(cos x) sin x)/(1−x^2 )))dx

$P l e a s e i n t e g r a t e$ $\int (\frac{e^{\cos x} \sin x}{1 - x^{2}}) d x$

Question Number 49661 Answers: 1 Comments: 2

calculateA_n =(1/(2i)) ∫_0 ^1 {(1+ix)^n −(1−ix)^n }dx

${c a l c u l a t e A}_{n} = \frac{1}{2 i} \int_{0}^{1} {{(1 + i x)}^{n} - {(1 - i x)}^{n}} d x$

Question Number 49646 Answers: 0 Comments: 0

calculate ∫∫_D (x^2 −y^2 )(√(x^2 +y^2 ))dxdy with D ={(x,y)∈R^2 / −1≤x≤1 and 0≤y≤2 }

$c a l c u l a t e \int \int_{D} (x^{2} - y^{2}) \sqrt{x^{2} + y^{2}} d x d y w i t h$ $D = {(x, y) \in R^{2} / - 1 ⩽ x ⩽ 1 a n d 0 ⩽ y ⩽ 2}$

Question Number 49645 Answers: 1 Comments: 0

calculate ∫∫_C ∣x+y∣dxdy with C=[−1,1]×[−1,1]

$c a l c u l a t e \int \int_{C} ∣ x + y ∣ d x d y w i t h C = [- 1, 1] \times [- 1, 1]$

Question Number 49636 Answers: 1 Comments: 2

1) calculate A_n =∫_0 ^∞ e^(−n[x]) sin(x)dx with n integr and n≥1 2) find nature of Σ_(n=1) ^∞ A_n

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

Question Number 49635 Answers: 1 Comments: 1

1)find f(x) =∫_0 ^(π/4) ((sint)/(2+x cos(2t)))dt 2) find g(x) =∫_0 ^(π/4) ((sint sin(2t)/((2+x cos(2t))^2 ))dx 3) find the value of ∫_0 ^(π/4) ((sint)/(2+3 cos(2t)))dt and ∫_0 ^(π/4) ((sin(t)sin(2t))/((2+3cos(2t))^2 ))dt

$1) f i n d f (x) = \int_{0}^{\frac{π}{4}} \frac{s i n t}{2 + x c o s (2 t)} d t$ $2) f i n d g (x) = \int_{0}^{\frac{π}{4}} \frac{s i n t s i n (2 t}{{(2 + x c o s (2 t))}^{2}} d x$ $3) f i n d t h e v a l u e o f \int_{0}^{\frac{π}{4}} \frac{s i n t}{2 + 3 c o s (2 t)} d t a n d \int_{0}^{\frac{π}{4}} \frac{s i n (t) s i n (2 t)}{{(2 + 3 c o s (2 t))}^{2}} d t$

Question Number 49457 Answers: 0 Comments: 0

evaluate ∫x^(3 ) J_3 (x)dx

$e v a l u a t e \int x^{3} J_{3} (x) d x$

Question Number 49392 Answers: 1 Comments: 0

Question Number 49367 Answers: 5 Comments: 5

a) ∫ (dx/(√(1−tgx))) b)∫ (dx/((1−tgx))^(1/3) ) c)∫ (dx/(√(1−(√(1−x)))))

$a) \int \frac{dx}{\sqrt{1 - tgx}}$ $b) \int \frac{dx}{\sqrt[3]{1 - tgx}}$ $c) \int \frac{dx}{\sqrt{1 - \sqrt{1 - x}}}$

Question Number 49344 Answers: 1 Comments: 1

let α>0 calculate ∫_(−∞) ^(+∞) (1+αi)^(−x^2 ) dx .

$l e t α > 0 c a l c u l a t e \int_{- \infty}^{+ \infty} {(1 + α i)}^{- x^{2}} d x .$

Question Number 49343 Answers: 0 Comments: 1

find ∫_0 ^1 ((ln(x))/(1+x))dx .

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

Question Number 49342 Answers: 0 Comments: 0

find ∫_0 ^1 (e^x /(1+x))dx .

$f i n d \int_{0}^{1} \frac{e^{x}}{1 + x} d x .$

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