Integration

• anpanman

  29 Sep 09, 21:37

  Differentiate sin^3 2x with respect to x and hence find cos^3 2x dx between pi/4 and 0. I got 1/3 as answer but the supposingly correct ans is 2/3.

  well what answer did you get?

   

  Next.

  Find the equation of the curve which has a gradient of (3x^2 -1)/x^2 and passes through the point (2,4)

  State the value approached by the gradient as x becomes increasingly large. ans:3.

  Dont really know what the equation is asking for in the later half.

• qdtimes2

  30 Sep 09, 01:03

  i got 1/3 for the 1st qn too

• wee_ws

  30 Sep 09, 06:26

  Originally posted by anpanman:

  Find the equation of the curve which has a gradient of (3x^2 -1)/x^2 and passes through the point (2,4)

  State the value approached by the gradient as x becomes increasingly large. ans:3.

  Dont really know what the equation is asking for in the later half.

  Hi,

    We are given that dy/dx = 3 - 1/x^2.

    "x becomes increasingly large" means x comes closer to infinity. When this happens, 1/x^2 approaches zero. Thus, dy/dx goes near to 3.

    Thanks!

  Cheers,
  Wen Shih

• Forbiddensinner

  30 Sep 09, 11:12

  Originally posted by anpanman:

  Differentiate sin^3 2x with respect to x and hence find cos^3 2x dx between pi/4 and 0. I got 1/3 as answer but the supposingly correct ans is 2/3.

  well what answer did you get?

   

  Next.

  Find the equation of the curve which has a gradient of (3x^2 -1)/x^2 and passes through the point (2,4)

  State the value approached by the gradient as x becomes increasingly large. ans:3.

  Dont really know what the equation is asking for in the later half.

  1/3