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 ( e^x + 2e^-x)²= e^2x+4+4e^-2xintegrate e^2x+4+4e^-2x with respect to x= 1/2(e^2x) + 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(e^2x) + 4x - 2e^2x]^ln4₀ = (1/2(e^{2ln4 (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)