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IntegrationQuestion and Answers: Page 236

Question Number 59825 Answers: 0 Comments: 0

Question Number 59803 Answers: 0 Comments: 3

Question Number 59802 Answers: 0 Comments: 1

Question Number 59800 Answers: 2 Comments: 0

find the general solution y(t) of the ordinary differential equation y′′ + ω^2 y=cos ωt ,where w>0

$f i n d t h e g e n e r a l s o l u t i o n y (t) o f t h e$ $o r d i n a r y d i f f e r e n t i a l e q u a t i o n$ $y^{″} + ω^{2} y = \cos ω t, w h e r e w > 0$

Question Number 59807 Answers: 1 Comments: 0

∫((x−1)/(√(2x−x^2 ))) dx

$\int \frac{x - 1}{\sqrt{2 x - x^{2}}} d x$

Question Number 59732 Answers: 2 Comments: 0

find I_n =∫ (dx/(sin^n x)) with n integr natural.

$f i n d I_{n} = \int \frac{d x}{{s i n}^{n} x} w i t h n i n t e g r n a t u r a l .$

Question Number 59679 Answers: 3 Comments: 0

Evaluate ∫_0 ^3 (((x^2 +3x)/x^3 ))

$E v a l u a t e$ $\underset{0}{\int^{3}} (\frac{x^{2} + 3 x}{x^{3}})$

Question Number 59659 Answers: 1 Comments: 5

Question Number 59647 Answers: 1 Comments: 1

Question Number 59631 Answers: 2 Comments: 3

1) calculate ∫_0 ^(2π) (dx/(acosx +bsinx)) with a , b reals 2)find also ∫_0 ^(2π) ((cosx dx)/((acosx +bsinx)^2 )) and ∫_0 ^(2π) ((sinx dx)/((acosx +bsinx)^2 )) 3) find the value of ∫_0 ^(2π) (dx/(2cosx +(√3)sinx))

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

Question Number 59576 Answers: 0 Comments: 4

let f(x) =∫ (dt/((x+t)(√(t^2 −x^2 )))) 1) determine a explicit form of f(x) 2) determine ∫ (dt/((x+2)(√(t^2 −4)))) and ∫ (dt/((x+1)(√(t^2 −1))))

$l e t f (x) = \int \frac{d t}{(x + t) \sqrt{t^{2} - x^{2}}}$ $1) d e t e r m i n e a e x p l i c i t f o r m o f f (x)$ $2) d e t e r m i n e \int \frac{d t}{(x + 2) \sqrt{t^{2} - 4}} a n d \int \frac{d t}{(x + 1) \sqrt{t^{2} - 1}}$

Question Number 59575 Answers: 1 Comments: 0

find ∫ ((sin(2x))/(1+cos^2 x))dx

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

Question Number 59563 Answers: 2 Comments: 1

Question Number 59528 Answers: 0 Comments: 5

let f(x) =∫_0 ^1 (dt/(1+xch(t))) with x real 1) determine a explicit form of f(x) 2)find also g(x)=∫_0 ^1 (dt/((1+xch(t))^2 )) 3) calculate ∫_0 ^1 (dt/(1+3ch(t))) and ∫_0 ^1 (dt/((1+3ch(t))^2 ))

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