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47.5 units^2The area underneath the curve bound by the axis being integrated with respect to (i.e. x axis)

2f-1=a

When tackling this question you cannot simply multiply what is in the bracket as this this is not fully expanded. First you must rewrite it as (x-2)(x-2). From here we can on expand the brackets by multip...

The product rule is used to differentiate this since we are trying to differentiate the product of 2 parts--x and ln(x)So using the product rule which is d/dx=u.(dv/dx) +v.(du/dx)let u=x and v=ln(x)then d...

Start with finding limits by setting 3x - x^2 = 0, then factorise x(3 - x) = 0. Therefore x = 0 or 3. The area is the integral of 3x - x^2 between x = 0 and 3, sub in 3 and 0 into 3(x^2)/2 - (x^3)/3, whic...