Question

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1. Find the area of the region bounded by the graphs of the given functions on the intervals indicated. a. y = x2 + 2, y = x, (2,5) b. y = (2x +1, y = 3x + 2, [0,2] C. y = ex-1, y = x,[1,4]

Answer 1

soi:- Given y=x+2,Y=X[2,5 - 5 A = [(**+2- 2+2-x) dx 2 5 2 5 5 A x? du tz fanufa ndu 2 2 5 A- 2 x +2[x JA [ (125-4 ) +2 (5-2) - < (25+4) - AC 69 2 Given y = √2x+1 ,723x+2 [0,2] A- (3x+2 vzatilda 2 2 2 2x+1 da A=3 Juda +2/dx - 0 5 du A - 3 lo 3[?]+2[*7; put u = (2x+ de la = 2 When x20, U Whena=2, u=5 A = 364-0 A - 34-0 ) + 2(2-0) (4-0) +2(2-0) - 4x}[u%2]. - 6 +4 5V5-1 3 AC Az 10 - 515-1 3

Given 06-1 y = e - X [1,4] A = 3(ex"ca) din * 4 4 A= ex- llad 4 122 éseada e 2 A selesai é ce? - - -* (16-17 a 15 Ile4-e) 2 A e A = e" - - 13