The figure below shows the graph of f (x) = 2 cos x + 1 Find the total area of t

Question

The figure below shows the graph of f (x) = 2 cos x + 1 Find the total area of thethree areas in gray, between the graph and the x-axis.

Explanation / Answer

The intersection points of the cutve y = x^3 - 5x^2 + 4x and y = 0 (x-axis) are x^3 - 5x^2 + 4x = 0 => x(x^2 - 5x + 4) = 0 => x(x - 4)(x - 1) = 0 x = 0, 1, 4 from 0 to 1 , the curve y = x^3 - 5x^2 + 4x will be on top of x-axis from 1 to 4, the x - axis will be on top of x^3 - 5x^2 + 4x area = ?(x^3 - 5x^2 + 4x - 0) from [0 to 1] + ?(0 - x^3 + 5x^2 - 4x ) dx from [ 1 to 4] => (1/4)x^4 - (5/3)x^3 + 2x^2 from [ 0 to 1] + -(1/4)x^4 + (5/3)x^3 - 2x^2 from [ 1 to 4] => [(1/4) - (5/3) + 2 ] + [ -64 +(320/3) - 32 - (-1/4 + (5/3) - 2) ] = [(1/4) - (5/3) + 2 - 64 +(320/3) - 32 + 1/4 - (5/3) + 2) ] = (1/2) - (10/3) + 4 - 96 + (320/3) = ( 3 - 20 + 24 - 576 + 640 ]/6 = 71/6 = 11.83 sq. units put your value and get the answer:

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