jonathan

integral of 1/2 (1+sin(6x))^2 dx

i got 1/2 integral of 1 + 2 sin(6x) + sin(6x)^2

i know 1 will be x .. and 2 sin (6x) will be - cos(6x) / 3 .. but i dont know what will be for sin(6x)^2

answer will be 1/2 (x - cos(6x)/3 + ???)

please explain thanks in advance

1 + 2 sin (6x) = 0

sin(6x) = -1/2

how would you get value for x please explain

r = 1 + 2sin(6x)

i have no clue how to do this.. if anyone can help thanks

http://img25.imageshack.us/img25/1886/81097140.png

i let x = tan(theta)

dx = sec(theta)^2 d(theta)

when x = 0 .. tan(theta) = 0 and theta = 0

when x = 1/2 .. tan(theta) = 1/2 and theta = ?

i m stuck from this point onward .. can anyone explain this problem to me

am not sure about substitution either.. whether it is x = tan(theta) or tan(2*theta)

please advise me on this thanks in advance

r = 1 / theta ; got to find when theta = pi

heres what i did ..

[(-theta)^-2 sin(theta) + theta^-1 cos(theta)] / [(-theta)^-2 cos(theta) - theta^-1 sin(theta)]

= (theta^-1 sin(theta) + cos(theta)) / (theta^-1cos(theta) - sin(theta))

= (1/pi sin(pi) + cos(pi)) / (1/pi cos(pi) - sin(pi))

= -1 / (-1/pi) = pi

is it correct? if not can u explain what i did wrong

thanks

so i have to tell whether this is convergent or divergent

http://img228.imageshack.us/img228/2289/27795158.p...

it's - infi on bottom and 2 on top of integral

so heres what i did...

limit as t approaches - infinity of integral t (bottom) to 2 (top) of (x e^(x/7) dx )

then i let u = x so du = dx and dV = e^(x/7) so V = 7e^(x/7)

now it becomes... after du / dv

= limit as t approaches - infinity [ x * 7 e^(x/7) ] t (bottom) to 2 (top) + integral t (bottom) to 2 (top) of (7 e^(x/7) dx )

= limit as t approaches - infinity [14 e^(2/7) - 7t e^(t/7)] + 7 [7 e^(x/7) ] t (bottom) to 2 (top)

= limit as t approaches - infinity [14 e^(2/7) - 7t e^(t/7)] + 7 [7 e^(2/7) - 7 e^(t/7) ]

= infinity

so its divergent

something is wrong but i m not able to figure it out .. can anyone help please

thanks

lim as x approaches 0 from negative side (-e ^ (1/x) )

why is it 0? can anyone explain..

thanks in advance

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I ended up with 0 / infinity which is 0 but am not sure if it's correct

can anyone solve it?

thanks in advance

lim as x approaches to infinity ( 1 + (1 / x)) ^ x

i got ..

e ^ lim as x approaches to infinity ln ( 1 + (1/x)) / 1/x

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A company that manufactures video cameras produces a basic model and a deluxe model. Over the past year, 45% of the cameras sold have been the basic model. Of those buying the basic model, 25% purchase an extended warranty, whereas 40% of all purchasers of the deluxe model buy an extended warranty. If you learn that a randomly selected purchaser bought an extended warranty, what is the probability that he or she has a basic model?

please explain

thx

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and

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Approximate the volume of material in a spherical shell of inner radius 5 centimeters and outer radius 5.125 centimeters.

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A circle is tangent to the y-axis at y = 3 and has one x-intercept at x = 1.

(a) Determine the other x-intercept. (b) Deduce the equation of the circle.

please explain that's what me lukin for mostly.. thanks

3 x^2 + 3x + 2y = 0

complete the square and reduce to one of the standard forms y - b = A ( x - a ) ^ 2 or x - a = A ( y - b) ^ 2

3 x^2 + 3x + 2y = 0

complete the square and reduce to one of the standard forms y - b = A ( x - a ) ^ 2 or x - a = A ( y - b) ^ 2