Evaluate `int_1^4 f(x)dx`, where `f(x)={(2x+8,1lex,le,2),(6x,2lex,le,4):}`

Evaluate: int_-2^2 f(x) dx where f(x)={:{(2x-1,-2 le x le1),(3x-2,1lex le2):}

Evaluate int_1^4 f(x)dx , where f(x)=|x-1|+|x-2|+|x-3|

Evaluate int_(1)^(4)f(x)dx , where f(x)={{:(4x+3,"if" 1 le x le 2),(3x+5,"if" 2 le x le 4.):}

Evaluate int_-1^1 f(x)dx , {(1,-,2x,x,le,0),(1,+,2x,x,ge,0):}

Two functions are defined as under : f(x)={(x+1, x le 1), (2x+1, 1 < x le 2):} and g(x)={(x^2, -1 le x le 2), (x+2, 2 le x le 3):} Find fog and gof

If f(x) is continuous in [0, 3], where f(x)={:{(3x-4", for " 0 le x le 2),(2x+k", for " 2 lt x le 3):} , then k=

Discuss the continous of the following function on its domain, where f(x)=x^(2)-4, "for" 0lex le2 =2x+3, "for" 2 ltx le4 =x^(2)-05, "for" 4 lt x le6.

Consider the functions f(x)={(x+1",",x le 1),(2x+1",",1lt x le 2):} and g(x)={(x^(2)",", -1 le x lt2),(x+2",",2le x le 3):} The range of the function f(g(x)) is