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IntegrationQuestion and Answers: Page 204

Question Number 74218 Answers: 1 Comments: 0

verify that y(x)=e^x (cos e^x −e^x sin e^x ) is the solution of integral equation y(x)=(1−xe^(2x) )cos 1−e^(2x) sin 1+∫_0 ^x {1−(x−t)e^(2x) }y(t)dt

$v e r i f y t h a t y (x) = e^{x} (\cos e^{x} - e^{x} \sin e^{x}) i s t h e s o l u t i o n o f i n t e g r a l e q u a t i o n y (x) = (1 - {x e}^{2 x}) \cos 1 - e^{2 x} \sin 1 + \underset{0}{\int^{x}} {1 - (x - t) e^{2 x}} y (t) d t$

Question Number 74210 Answers: 1 Comments: 0

∫e^t cos e^t dt

$\int e^{t} \cos e^{t} d t$

Question Number 74131 Answers: 0 Comments: 2

Can anyone share the solutions (pdf) of the book Advanced engineering Mathematics by Erwin kreyzig 8th edition ?

$C a n a n y o n e s h a r e t h e s o l u t i o n s (p d f)$ $o f t h e b o o k A d v a n c e d e n g i n e e r i n g$ $M a t h e m a t i c s b y E r w i n k r e y z i g 8 t h$ $e d i t i o n ?$

Question Number 74117 Answers: 0 Comments: 1

Find the volume of the solid that lies within the sphere x^2 +y^2 +z^2 =16, above the x-y plane and below the cone z=(√(x^2 +y^2 ))

$F i n d t h e v o l u m e o f t h e s o l i d t h a t l i e s$ $w i t h i n t h e s p h e r e x^{2} + y^{2} + z^{2} = 16, a b o v e$ $t h e x - y p l a n e a n d b e l o w t h e c o n e$ $z = \sqrt{x^{2} + y^{2}}$

Question Number 74068 Answers: 1 Comments: 4

Question Number 74040 Answers: 1 Comments: 1

Find orthogonal trajectories of the curves: (x−c)^2 +y^2 =c^2 .

$F i n d o r t h o g o n a l t r a j e c t o r i e s o f t h e$ $c u r v e s : {(x - c)}^{2} + y^{2} = c^{2} .$

Question Number 74037 Answers: 1 Comments: 0

∫_0^ ^(Π/2) xcos^n xdx by reduction formula

$\int_{0^{}}^{Π / 2} x \cos^{n} x d x b y r e d u c t i o n f o r m u l a$

Question Number 73832 Answers: 2 Comments: 7

Question Number 74338 Answers: 0 Comments: 0

∫e^(2t) sin e^t dt

$\int e^{2 t} \sin e^{t} d t$

Question Number 73804 Answers: 0 Comments: 0

Question Number 73751 Answers: 1 Comments: 1

Find out the value of J=∫_0 ^∞ ∫_0 ^1 (2e^(−2xy) −e^(−xy) )dxdy

$F i n d o u t t h e v a l u e o f$ $J = \int_{0}^{\infty} \int_{0}^{1} (2 e^{- 2 x y} - e^{- x y}) d x d y$

Question Number 73715 Answers: 1 Comments: 2

Evaluate the integral : ∫_( R) ∫(3x^2 +14xy+8y^2 )dxdy for the region R in the 1st quadrant bounded by the lines y=((−3)/2)x+1,y=((−3)/2)x+3,y=−(1/4)x and y=−(1/4)x+1 .

$E v a l u a t e t h e i n t e g r a l :$ $\int_{R} \int (3 x^{2} + 14 x y + 8 y^{2}) d x d y f o r t h e r e g i o n$ $R in t h e 1 s t q u a d r a n t b o u n d e d b y t h e$ $l i n e s y = \frac{- 3}{2} x + 1, y = \frac{- 3}{2} x + 3, y = - \frac{1}{4} x$ $a n d y = - \frac{1}{4} x + 1 .$

Question Number 73689 Answers: 2 Comments: 0

∫_(−1) ^( 1) (2+x)sin^(−1) (((√(3−3x^2 ))/(2+x)))dx = ?

$\int_{- 1}^{1} (2 + x) \sin^{- 1} (\frac{\sqrt{3 - 3 x^{2}}}{2 + x}) d x = ?$

Question Number 73545 Answers: 1 Comments: 2

evaluate ∫lnx dx

$e v a l u a t e \int l n x d x$

Question Number 73489 Answers: 0 Comments: 0

calculate ∫_0 ^∞ ((arctan(3+x^2 ))/((2 x^2 +9)^2 ))dx

$c a l c u l a t e \int_{0}^{\infty} \frac{a r c t a n (3 + x^{2})}{{(2 x^{2} + 9)}^{2}} d x$

Question Number 73484 Answers: 1 Comments: 0

decompose inside C(x) the fraction F(x)=(1/((x^2 +1)^n )) calculate ∫_0 ^∞ F(x)dx

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

Question Number 73483 Answers: 1 Comments: 0

find ∫ (dx/(x+2−(√(x^2 −x +7))))

$f i n d \int \frac{d x}{x + 2 - \sqrt{x^{2} - x + 7}}$

Question Number 73482 Answers: 1 Comments: 1

find ∫ (dx/((√(x^2 +1))+(√(x^2 +3))))

$f i n d \int \frac{d x}{\sqrt{x^{2} + 1} + \sqrt{x^{2} + 3}}$

Question Number 73481 Answers: 0 Comments: 0

find ∫ ln(x−cosx)dx

$f i n d \int l n (x - c o s x) d x$

Question Number 73480 Answers: 0 Comments: 0

find ∫_0 ^∞ xe^(−x^2 ) arcran(x+(1/x))dx

$f i n d \int_{0}^{\infty} {x e}^{- x^{2}} a r c r a n (x + \frac{1}{x}) d x$

Question Number 73479 Answers: 1 Comments: 1

find ∫ ((3x+2)/((x+1)^2 (x−2)^3 ))dx

$f i n d \int \frac{3 x + 2}{{(x + 1)}^{2} {(x - 2)}^{3}} d x$

Question Number 73478 Answers: 1 Comments: 0

find ∫_0 ^1 ((x^3 −3)/(√(x^2 −x +2)))dx

$f i n d \int_{0}^{1} \frac{x^{3} - 3}{\sqrt{x^{2} - x + 2}} d x$

Question Number 73477 Answers: 1 Comments: 0

calculate ∫ ((x^3 −4x+5)/(x^2 −x +1))dx

$c a l c u l a t e \int \frac{x^{3} - 4 x + 5}{x^{2} - x + 1} d x$

Question Number 73428 Answers: 1 Comments: 2

Evaluate : 1) ∫_(−2) ^( 2) ∫_(−(√(4−x^2 ))) ^( (√(4−x^2 ))) (3−x)dydx . (after changing the integral to polar form). 2) ∫_0 ^4 ∫_0 ^(4−x) ∫_0 ^( 4−(y^2 /4)) dzdydx .

$E v a l u a t e :$ $1) \int_{- 2}^{2} \int_{- \sqrt{4 - x^{2}}}^{\sqrt{4 - x^{2}}} (3 - x) d y d x .$ $(a f t e r c h a n g i n g t h e i n t e g r a l t o p o l a r f o r m) .$ $2) \int_{0}^{4} \int_{0}^{4 - x} \int_{0}^{4 - \frac{y^{2}}{4}} d z d y d x .$

Question Number 73429 Answers: 1 Comments: 3

Solve : ∫(([cos^(−1) x(√(1−x^2 ))]^(−1) )/(log_e [2+((sin(2x(√(1−x^2 ))))/π)]))dx Evaluate ∫_(−π/2) ^( π/2) sin^2 xcos^2 x(cosx+sinx)dx

$S o l v e : \int \frac{{[{c o s}^{- 1} x \sqrt{1 - x^{2}}]}^{- 1}}{{l o g}_{e} [2 + \frac{s i n (2 x \sqrt{1 - x^{2}})}{π}]} d x$ $E v a l u a t e \int_{- π / 2}^{π / 2} {s i n}^{2} {x c o s}^{2} x (c o s x + s i n x) d x$

Question Number 73397 Answers: 1 Comments: 1

find f(x)=∫_0 ^1 e^(−t) ln(1−xt^2 )dt with ∣x∣<1 2)calculate ∫_0 ^1 e^(−t) ln(1−(t^2 /2))dt

$f i n d f (x) = \int_{0}^{1} e^{- t} l n (1 - {x t}^{2}) d t w i t h ∣ x ∣< 1$ $2) c a l c u l a t e \int_{0}^{1} e^{- t} l n (1 - \frac{t^{2}}{2}) d t$

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