Search over 10,000 free study notes

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...

2x² - 2y = 282y - 4 = 12x
y - 2 = 6xy = 6x + 2
Substitute y = 6x + 2
2x² - 2(6x + 2) = 282x² - 12x - 4 = 282(x² - 6x - 2) = 28x² - 6x ...

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...