Hey, couldn't wrap my head around these questions:

QUESTION 14. Integral of x^n.sin(x) dx for limits 0 to 1.

(a) Does not exist

(b) Is necessarily greater than 1

(c) Is greater than 1/(n + 1)

(d) Is less than 1/(n + 1)

Can anyone show the steps for solving this?

QUESTION 23. Consider a homogenous goods market with the demand

function Q = 30 P, where Q and P denote quantity and price respectively.

There are two firms playing a price game in the following manner: rm 1

quotes a price and then rm 2 chooses a price. When they charge the same

price they share the market equally and otherwise the market demand goes

to the firm charging lower price. Firm 1 has a capacity constraint at the

output level 5 units such that upto five units the marginal cost of production

is Rs 3 per unit of output, however beyond 5 units it cannot produce any

output. Firm 2 does not have any capacity constraint, it can produce any

amount with the marginal cost Rs 6. What would be the equilibrium price

in the market?

(a) 3

(b) 6

(c) 6 -e , where e is very small positive number

(d) 3 +e , where e is very small positive number

QUESTION 46. What is the total number of local maxima and local min-

ima of the following function

f(x) =(2 + x)^3 if -3 <x<= -1

x^2/3 if -1<x< 2

(a) 1

(b) 2

(c) 3

(d) 4

Also questions 36 and 39 part A of DSE 2012.

The questions have too many cumbersome signs for it to simply copy and paste so here's the link:

http://econdse.org/wp-content/uploads/2012/07/2012-Option-A.pdfOnce again, any help is greatly appreciated.