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IntegrationQuestion and Answers: Page 249

Question Number 50384 Answers: 1 Comments: 1

find ∫ (dx/((1−x^2 )(1−x^3 ))) 2) calculate ∫_2 ^(√5) (dx/((1−x^2 )(1−x^3 )))

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

Question Number 50219 Answers: 7 Comments: 0

Question Number 50423 Answers: 1 Comments: 1

find f(a) =∫_a ^(+∞) (dx/((1+x^2 )(√(x^2 −a^2 )))) with a>0

$f i n d f (a) = \int_{a}^{+ \infty} \frac{d x}{(1 + x^{2}) \sqrt{x^{2} - a^{2}}} w i t h a > 0$

Question Number 50186 Answers: 1 Comments: 0

Let f(x)= ∫_2 ^( x) (dt/(1+t^6 )). Prove that : (1/(730))<f(3)<(1/(65)).

$L e t f (x) = \int_{2}^{x} \frac{d t}{1 + t^{6}} .$ $P r o v e t h a t : \frac{1}{730} < f (3) < \frac{1}{65} .$

Question Number 50161 Answers: 1 Comments: 0

Find the function whose first derivative is 8−(5/(x^2 )^(1/3) ) the initial conditions f(8)=−20

$F i n d t h e f u n c t i o n w h o s e f i r s t$ $d e r i v a t i v e i s 8 - \frac{5}{\sqrt[3]{x^{2}}} t h e i n i t i a l$ $c o n d i t i o n s f (8) = - 20$

Question Number 50158 Answers: 7 Comments: 1

Question Number 50052 Answers: 5 Comments: 1

Question Number 50007 Answers: 1 Comments: 1

For a < x < b, find ∫_a ^b (√(x−a)) . (√(b−x)) dx

$For a < x < b, find$ $\underset{a}{\int^{b}} \sqrt{x - a} . \sqrt{b - x} d x$

Question Number 49968 Answers: 0 Comments: 1

find f(x) =∫_0 ^(+∞) ((t arctan(xt))/(1+t^4 )) dt

$f i n d f (x) = \int_{0}^{+ \infty} \frac{t a r c t a n (x t)}{1 + t^{4}} d t$

Question Number 49967 Answers: 0 Comments: 1

calculate ∫_0 ^(+∞) (dx/((x^2 −i)^2 ))

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

Question Number 49956 Answers: 1 Comments: 1

find ∫_0 ^1 cos(n arcosx)dx with n integr natural.

$f i n d \int_{0}^{1} c o s (n a r c o s x) d x w i t h n i n t e g r n a t u r a l .$

Question Number 49953 Answers: 0 Comments: 3

1) calculate ∫_0 ^1 ln(1+ix)dx and ∫_0 ^1 ln(1−ix)dx 2) find the value of ∫_0 ^1 ln(1+x^2 )dx .

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

Question Number 49950 Answers: 1 Comments: 1

Question Number 49954 Answers: 1 Comments: 1

find f(α) =∫_0 ^1 ((arctan(αx))/(1+α^2 x^2 ))dx 2) calculate ∫_0 ^1 ((arctan(2x))/(1+4x^2 )) dx and ∫_0 ^1 ((arctan(3x))/(1+9x^2 )) dx .

$f i n d f (α) = \int_{0}^{1} \frac{a r c t a n (α x)}{1 + α^{2} x^{2}} d x$ $2) c a l c u l a t e \int_{0}^{1} \frac{a r c t a n (2 x)}{1 + 4 x^{2}} d x a n d \int_{0}^{1} \frac{a r c t a n (3 x)}{1 + 9 x^{2}} d x .$

Question Number 49942 Answers: 0 Comments: 1

calculate ∫∫_D (√(x^4 −y^4 ))dxdy with D =[0,1]×[0,1]

$c a l c u l a t e \int \int_{D} \sqrt{x^{4} - y^{4}} d x d y$ $w i t h D = [0, 1] \times [0, 1]$

Question Number 49941 Answers: 0 Comments: 3

calculate ∫_0 ^1 e^(−x) ln(1+x)dx

$c a l c u l a t e \int_{0}^{1} e^{- x} l n (1 + x) d x$

Question Number 49939 Answers: 0 Comments: 4

find ∫_0 ^(π/2) sinx ln(1+x) dx

$f i n d \int_{0}^{\frac{π}{2}} s i n x l n (1 + x) d x$

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

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

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