The rate of change of weight of person w in kg with respect to their height h in centimetres is given approximately by \({dw\over dh}=4.364 \times 10^{-5}h^2\). Find weight as a function of height. Also find the weight of a person whose height is 150 cm.

A tree is growing so that, after t - years its height is increasing at a rate of \({18\over \sqrt{t}}\) cm per year Assume that when t = 0, the height is 5 cm.
(i) Find the height of the tree after 4 years.
(ii) After how many years will the height be 149 cm?

Integrate the following functions with respect to x : \((3x+4)\sqrt{3x+7}\)

Integrate the following functions with respect to x :\({1\over (x-1)(x+2)^2}\)

Integrate the following with respect to x : \(x^3 e^{-x}\)

Integrate the following with respect to x : 27 x²e^3x

Integrate the following with respect to x : x²cos x

Evaluate the following integrals : \(\int e^x({1-x\over 1+x^2})^2 dx\)

Evaluate the following integrals : \(\int{2x+3\over \sqrt{x^2+x+1}}dx\)

Integrate the following with respect to x : \({3x+1\over 2x^2-2x+3}\)