Question

1) Find the following indefinite integrals.

    a) (4-3xsec^2 x)/x dx

    b) (5 sin^ 3 x ) / (1+cosx)(1-cosx) dx

2) A particle starts from rest and moves along the x-axis from the origin at t = 0 with acceleration

       a(t) =   6 - 2t (ms^-2) at time t. When and where will it come to rest.

       Remember dvdt = acceleration and dsdt = velocity

3) Use substitution to find the following integrals.

    a) (9x)/ sqrt of (3+x2) dx                         Let U = 3+x^2

    b) (dx) / (25- x^2 ) Let x = 5 sin U

4) Consider the integral 1∞ 1 / (2x+1)^3 dx.

    a) Explain why the integral is improper.

    b) Determine whether the integral is convergent or divergent and if convergent, evaluate he integral. (Show all working)

Answer 1