Question

Hi, can show with workings, By the method of substitution, evaluate the definite integral,

∫[b,a] t / √(t-1) dt
when a = 6.2, b = 12.6 with t > 1. Give your answer to 3 decimal places.

Answer 1

let u = t-1 then du/dt = 1 then du = dx

from the initial substitution u = t -1 then t = u -1

so the problem becomes \[\int\limits_{?}^{?} ( u + 1) \times u^{1/2} du\]

simplifying it is

\[\int\limits_{?}^{?} u^{3/2} - u^{1/2} du\]

should be easy enough to integrate then replace u with t -1