What happens to the level of consumer surplus as the price of a good falls?

The demand curve for product X is given by Qdx=460-4Px

1. How much consumer surplus do consumers receive when Px=$35?
The back of the book says the answer should be $12,800 but I don’t understand how to arrive at that answer.

2. In general, what happens to the level of consumer surplus as the price of a good falls?

As the price of a good falls the consumer surplus rises. The area for consumer surplus is that small triangle just below the demand curve but above the price line. First of all, from the demand equation, lets calculate the value of Px when Qdx is set to 0. This will give you 115. Now if you plot all these on a graph with a downword sloping demand curve you will have two price level on the vertical axis,i.e. one at $35 (equilibrium price) and the other one is 115 (the price at which there is no demand for X). On the horizontal axis you can simply calculate the Quantity demanded when the price is $35 which is equal to 320.Ok now you can easily find the area for the small triangle (consumer surplus) which has a height of 80 (115-35) and a base of 320. From basic maths, area of triangle = 1/2*base*height:

Therefore, consumer surplus = 1/2 (80) (320) = 12800