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Question Number 53 by surabhi last updated on 25/Jan/15
Evaluate ∫_1 ^4 (((x^2 +x))/( (√(2x+1))))dx
Evaluate∫14(x2+x)2x+1dx
Answered by surabhi last updated on 04/Nov/14
[(x^2 +x)∙(√(2x+1))]_2 ^4 −∫_2 ^4 (2x+1)∙(√(2x+1))dx =(60−6(√5))−∫_2 ^4 (2x+1)^(3/2) dx =(60−6(√5))−(1/5)[(2x+1)^(5/2) ]_2 ^4 =(60−6(√5))−[((243)/5)−5(√5)] =((57)/5)−(√5)
[(x2+x)⋅2x+1]24−∫24(2x+1)⋅2x+1dx=(60−65)−∫24(2x+1)3/2dx=(60−65)−15[(2x+1)5/2]24=(60−65)−[2435−55]=575−5

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