wing asked in 科學及數學數學 · 1 decade ago


New Trend Additional Mathematics

Revision Exercise 20


In Fig. 14, the shaded region is bounded by the curves y=cos x,y=sin 2x, and the x-axis within the range (x is equal or bigger that 0 and

pai/2 is smaller or equal than x)

(a) Find the coordinates of P

(b) If the region is rotated about the x-axis ,find the volume of the solid generated in term of pai.

1 Answer

  • 1 decade ago
    Favorite Answer


    cos x =sin 2x

    cos x =2sinxcosx


    cosx=0 or sinx=1/2

    x= π/2 or π/6

    y= 0 or √3/2




    The volume of the solid generated

    =π∫(cos^2 x-sin^2 2x) dx from [0 to π/6]

    =π∫(cos^2 x- 4sin^2 xcos^2 x) dx

    = π∫(4cos^4 x- 3cos^2 x) dx

    Let In=∫(cos^n x) dx

    ∫(cos^2 x) dx

    =(sin x cos x)/2+(1/2) I0 [x from 0 to π/6]



    ∫(cos^4 x) dx

    =(sin x cos^3 x)/4+(3/4) I2 [x from 0 to π/6]



    π∫(4cos^4 x- 3cos^2 x) dx



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