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So u=2+lnx, therefore du/dx=1/x , we can work out the new upper and new lower limit by substitute in e and 1 into 2+lnx , and we get 2+ln(e)=3 , 2+ln(1)=2Rearrange the differential we get dx=xdu , substit...

x²-5x+4 <0First we ignore the inequality and try to solve the equation x²-5x+4=0, which we do via factorising (x-4)(x-1)=0. x = 4 or x=1We draw the graph using our solution, going...

Call the two numbers x and y. The constraint is that x + y =100, and we need to maximise A=xy.
Rearrange the constraint to y = 100 - x, and substitute into the product equation.
A = x(100-x) = ...

First, since there are terms with different factors of x summing together, we can separate these into three individual integrals as follows:int(x³ dx) + 4int(x²dx) + int(sinx dx)Then...

i) let dy/dx = ans, where ans = y, where you multiply the coefficients of each constant of x by the power and reduce the power by 1 in the equation ytherefore dy/dx = 2x - 2 - 12x^-1/2ii) repeat...