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Since our function is a product of two "mini-functions" of x, we are able to use integration by parts.The trick for this is to correctly set 'u' and 'dv'. 'u' should be labelled as the function ...

The answer is 2/3. This can either be obtained by performing a standard integration of y=x^2, using the power rule, between x = 1 and x = -1. Alternatively, integrate y = x^2 between x = 0 and x = 1, then...

First, factorise the equation into y = (x+3)(x-2)(x+2), nothing that x²-4 is the difference of two squares so is easy to factorise. From the factorised equation, the points at which the curve...

S= 0.5n(n+1) ( formula for the sum of the first n natural numbers) 0.5K(K+1)= 300 ( sub in K and make the formula equal to the total sum given) 0.5K(K+1)-300= 0 ( take away 300 from both sides) ...

dy/dx = 2x - 2 -12x^-1/2dy/dx = 02x - 2 - 12x^-1/2 = 0x = 4 (stationary point)d²y/dx²= 2 + 6x^-3/2when x=4, d²y/dx²= 11/411/4 >...