The finite region S is bounded by the y-axis, the x-axis, the line with equation x = ln4 and the curve with equation y = ex + 2e–x , (x is greater than/equal to 0). The region S is rotated through 2pi radians about the x-axis. Use integration to find the

formula for volume of solid generated = 2pi x integral between limits of y2expand ( ex + 2e-x)2= e2x+4+4e-2xintegrate e2x+4+4e-2x with respect to x= 1/2(e2x) + 4x - 2e-2x (+C) however c won't be used as we are integrating between valuesuse the limits 0 and ln4 (given in the question) [1/2(e2x) + 4x - 2e2x]ln40 = (1/2(e2ln4 (which is ln16)) + 4ln4 - 2e-2ln4 (which is ln(1/16)) )-(1/2(e0) + 4(0) - 2e0)= (8 + 4ln4 - 1/8) - (1/2-2)= 75/8 +4ln4times all by pi = pi(75/8 + 4ln4)

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Answered by Kit T. Maths tutor

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