integral calculus

Integrate (((cos^2(x)*sin(x)/(1-sin(x)))-sin(x))dx

thanks

  1. 👍 0
  2. 👎 0
  3. 👁 59
asked by Mycah
  1. If (((cos^2(x)*sin(x)/(1-sin(x)))-sin(x)) mean:

    cos ^ 2 (x) * sin (x) / [ 1 - sin(x) ] - sin (x)

    then:

    cos ^ 2 (x) * sin (x) / [ 1 - sin(x) ] - sin (x) =

    sin (x) * { cos ^ 2 (x) / [ 1 - sin(x) ] - 1 } =

    sin (x) * { [ 1 - sin ^ 2 (x) ] / [ 1 - sin(x) ] - 1 } =

    sin (x) * { [ 1 + sin (x) ] * [ 1 - sin(x) ] / [ 1 - sin(x) ] - 1 } =

    sin (x) * [ 1 + sin(x) - 1 ] =

    sin (x) * sin (x) = sin ^ 2 (x)


    cos ^ 2 (x) * sin (x) / ( 1 - sin(x) ) - sin (x) = sin ^ 2 (x)


    Integrate [ cos ^ 2 (x) * sin (x) / ( 1 - sin(x) ) - sin (x) ] dx = Integrate sin ^ 2 (x) dx = x / 2 + sin (2x) / 4 + C

    1. 👍 0
    2. 👎 0
    posted by Bosnian
  2. Hmmm. I get x/2 - sin(2x)/4

    1. 👍 0
    2. 👎 0
    posted by Steve
  3. My typo.

    Integrate sin ^ 2 (x) dx = x / 2 - sin (2x) / 4 + C

    1. 👍 0
    2. 👎 0
    posted by Bosnian

Respond to this Question

First Name

Your Response

Similar Questions

  1. Maths

    Question : Integrate [x/(1+(sin a*sin x))] from 0 to pi My first thought was to apply integrate f(x) dx= f(a-x) dx method Which simplified the integral into; 2I = integrate [pi/(1+(sin a*sin x))] dx , cancelling out x Then I made

    asked by Ashley on March 18, 2019
  2. TRIG!

    Posted by hayden on Monday, February 23, 2009 at 4:05pm. sin^6 x + cos^6 x=1 - (3/4)sin^2 2x work on one side only! Responses Trig please help! - Reiny, Monday, February 23, 2009 at 4:27pm LS looks like the sum of cubes sin^6 x +

    asked by hayden on February 23, 2009
  3. tigonometry

    expres the following as sums and differences of sines or cosines cos8t * sin2t sin(a+b) = sin(a)cos(b) + cos(a)sin(b) replacing by by -b and using that cos(-b)= cos(b) sin(-b)= -sin(b) gives: sin(a-b) = sin(a)cos(b) - cos(a)sin(b)

    asked by Pablo on November 26, 2006
  4. algebra

    Can someone please help me do this problem? That would be great! Simplify the expression: sin theta + cos theta * cot theta I'll use A for theta. Cot A = sin A / cos A Therefore: sin A + (cos A * sin A / cos A) = sin A + sin A = 2

    asked by Valerie on February 18, 2007
  5. Mathematics-Integration

    Question: Prove that [integrate {x*sin2x*sin[π/2*cos x]} dx] /(2x-π) } from (0-π) = [ integrate {sin x*cos x*sin[π/2*cos x} dx ] from (0-π). My thoughts on the question: We know that integrate f(x) dx from (0-a) = integrate

    asked by Shenaya on June 8, 2017
  6. trig

    Reduce the following to the sine or cosine of one angle: (i) sin145*cos75 - cos145*sin75 (ii) cos35*cos15 - sin35*sin15 Use the formulae: sin(a+b)= sin(a) cos(b) + cos(a)sin(b) and cos(a+b)= cos(a)cos(b) - sin(a)sin)(b) (1)The

    asked by Paul C on November 26, 2006
  7. Mathematics - Trigonometric Identities

    Let y represent theta Prove: 1 + 1/tan^2y = 1/sin^2y My Answer: LS: = 1 + 1/tan^2y = (sin^2y + cos^2y) + 1 /(sin^2y/cos^2y) = (sin^2y + cos^2y) + 1 x (cos^2y/sin^2y) = (sin^2y + cos^2y) + (sin^2y + cos^2y) (cos^2y/sin^2y) =

    asked by Anonymous on November 8, 2007
  8. Trigonometry

    Solve the equation for solutions in the interval 0

    asked by Renee on March 7, 2016
  9. Calculus

    Integrate 1/sinx dx using the identity sinx=2(sin(x/2)cos(x/2)). I rewrote the integral to 1/2 ∫ 1/(sin(x/2)cos(x/2))dx, but I don't know how to continue. Thanks for the help. Calculus - Steve, Tuesday, January 12, 2016 at

    asked by Andre-Steve, please reply on January 12, 2016
  10. math

    Prove that for all real values of a, b, t (theta): (a * cos t + b * sin t)^2

    asked by mathstudent on December 19, 2006
  11. math

    Eliminate the parameter (What does that mean?) and write a rectangular equation for (could it be [t^2 + 3][2t]?) x= t^2 + 3 y = 2t Without a calculator (how can I do that?), determine the exact value of each expression. cos(Sin^-1

    asked by Anonymous on August 3, 2007

More Similar Questions