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 fromthe 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 LetU = 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 isconvergent or divergent and if convergent, evaluate he integral.(Show all working)
