under the topic market equilibrium under fixed no of firms and the subtopic changes in market demand (increase in market demand). it says that if the demand increased then the demand curve D2D2 will shift rightwards . this will result inthe increased competion among buyers which will increase the price.and new equilibrium is achieved at E2 . BUT BUT BUT why will the price increase because as stated in the law of demand if the quantity demanded increased then the price should fall!!!!!!!!!!!! but why will the price increase in this case??????????????

Law of demand explains the inverse relationship between price of a good and it quantity demanded. An increase in price causes the demand of a good to contract, and, a fall in the price of a good causes the demand to expand. In both the cases, the demand curve of the consumer does not shift rightwards(or leftwards)  as the demand is only expanding/contracting  and not increasing/decreasing.

But, In case of market equilibrium, we study increase/decrease in demand, rather than expansion/contraction in demand. An increase/decrease in demand is the result of changes in factors affecting demand, other than the price of the commodity such as changes in income of the consumer, change in price of related goods etc. In the given case of change in demand(under market equilibrium), demand increases from D₁ to D₂  which results in the increase in market price since the market supply was constant.