HI, Uni starts next week and we have a first week paper to test our weaknesses. Integration has been a struggle at times but with the mock paper they have provided I am amiss with these 4 questions - sometimes not even understanding the actual question . Apologies for my notaion...

Any help would be greatly appreciated.

(i) Given that f & g are continous and that I = f(x) dx = 5 (limts 6 & 2) and I = g(x) dx = 9 (limits 6 & 2) calculate I = 4f(x) - g(x) dx (limits 2 & 6)

(ii) Using method by parts to express I = y^2*log(y) dy (limits x & 1) in the form

A(x) + I= B(y) dy (limits x & 1)

(iii) Integrate I = ((9x^2)/((1-x^3)^0.5)) by using substitution u = 1 - x^3

(iv) Find a suitable substitution of the form y = f(x) for I = x^3*e^(-x^2) dx (limits infinity & 0)