Using the substitution of u=6x+5 find the value of the area under the curve f(x)=(2x-3)(6x+%)^1/2 bounded between x=1 and x=1/2 to 4 decimal places.
dx=du/6 => (u-5)/6=x So the integral is now (2((u-5)/6)-3)(u^1/2) du/6 Which through simplifying becomes (1/36)(2u-28)(u^1/2)du = (1/36)(2u^3/2 -28u^1/2)du After integrating becomes (1/36)(4(u^5/2)/5 -56(u^3/2)/3) Bounded between u=11 and u=8 by the substitution After evaluating we reach our final answer of -2.2889 to 4dp
JT
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