Shillong (pronʃɪˈlɒŋ) is a hill station and the capital of Meghalaya, a state in northeastern India. It is the headquarters of the East Khasi Hills district. Shillong is the 330th most populous city in India with a population of 143,229 according to the 2011 census. It is said that the rolling hills around the town reminded the British of Scotland. Hence, they would also refer to it as the "Scotland of the East".
Shillong has steadily grown in size since it was made the civil station of the Khasi and Jaintia Hills in 1864 by the British. In 1874, on the formation of Assam as the Chief Commissioner's Province, it was chosen as the headquarters of the new administration because of its convenient location between the Brahmaputra and Surma valleys and more so because the climate of Shillong was much cooler than tropical India. Shillong remained the capital of undivided Assam until the creation of the new state of Meghalaya on 21 January 1972, when Shillong became the capital of Meghalaya, and Assam moved its capital to Dispur in Guwahati.
Shillong was capital for composite Assam during the British regime and later till a separate State of Meghalaya was formed. David Scott, the British civil servant of the East India Company, was the Agent of the Governor-General North East Frontier. During the First Anglo-Burmese War the British authorities felt the need for a road to connect Sylhet and Assam. The route was to traverse across the Khasi and Jaintia Hills. David Scott overcame the difficulties his administration faced from the opposition of the Khasi Syiems – their chiefs and people. Impressed by the favourable cool climate of Khasi Hills, they negotiated with the Syiem of Sohra in 1829 for a sanatorium for the British. Thus began the consolidation of British interests in the Khasi-Jaintia Hills.
A serious uprising by the Khasis against foreign occupation of their land followed. It began early in 1829 and continued till January 1833. Eventually, the Khasi confederate chiefs were no match against the military might of the British.
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Guwahati (en assamais : গুৱাহাটী ; en hindi : गुवाहाटी) antérieurement Gauhatî, — du sanskrit, guwa, « noix d'arec » et « haat », « le marché » — est la plus importante ville de l'Assam, État indien situé au nord-est du pays. La ville sert aussi de centre culturel, capitale politique et commerciale pour la région. Elle est considérée traditionnellement comme le lieu de naissance du dieu Kâma. La capitale de l'État, Dispur, n'est qu'une de ses banlieues. thumb|left|600px| Vue de Guwahati.
Aizawl (pronaɪˈzɔːl; Mizo: ˈʌɪ̯.ˈzɔːl) is the capital of the state of Mizoram in India. Aizawl was officially established on 25 February 1890. With a population of 293,416, it is the largest city in the state. It is also the centre of administration containing all the important government offices, state assembly house and civil secretariat. The population of Aizawl strongly reflects the different communities of the ethnic Mizo people. In 1871–72, the disorderly conduct of Khalkom, a Mizo Chief, compelled the British to establish an outpost that later became the Aizawl Village.
vignette|Une carte des "Sept États sœurs". Le Nord-Est indien est une zone géographique de la République indienne formant une communauté politique et économique de huit États au nord-est de celle-ci. Il regroupe le Sikkim, l'Arunachal Pradesh, l'Assam, Manipur, le Meghalaya, Mizoram, le Nagaland et Tripura. Cette zone est linguistiquement et culturellement très différente de ce que l'on rencontre dans le reste de l'Inde. Un grand nombre d'habitants de ces États parlent des langues tibéto-birmanes et ont une culture proche de celle des autres pays d'Asie du Sud-Est et du Tibet.
Explore le concept d'intégrabilité de Lebesgue et les critères d'intégrabilité de Lebesgue, en soulignant l'importance des intégrales supérieures et inférieures.