b) \( \int_{1}^{3} \int_{x}^{x^{2}} \int_{0}^{\ln x} x e^{y} d y d z d x \)

A particle \( P \) moves in a straight line so that, \( t \) seconds after passing a fixed point \( O \), its displacement, \( s \) metres, is given by \( s=4 t^{3}-15 t^{2}+18 t \). Find (i) the velocity of \( P \) when \( t=3 \), (ii) the acceleration of \( P \) when \( t=3 \), (iii) the values of \( t \) when \( P \) is at instantaneous rest, (iv) the distance travelled by \( P \) in the first 2 seconds of its motion, (v) the distance of \( P \) from \( O \) when \( t=2 \).

1. \( y=\left(x^{2}+2 x\right)^{x^{2}-2 x} \) ise \( \frac{d y}{d x}= \) ?

Given \( \mathrm{TP}=90 \mathrm{~K}^{2}-\mathrm{K}^{3} \) find a. Marginal product b. Average product c. The value of output which equates average product and marginal product

\( \int \frac { d x } { x ^ { r } + 4 x + 11 } \)

3. Given \( T P=90 \mathrm{~K}^{2}-\mathrm{K}^{3} \) find a. Marginal product b. Average product c. The value of output which equates average product and marginal product