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

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)=|x-1|+|x-2|+|x-3|

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

Evaluate : int_(0)^(3) f(x) dx , where f(x)={(cos2x",",0 le x le (pi)/(2)),(3",",(pi)/(2) le x le 3):}

Evaluate: (i) \int_(-1)^1f(x)dx ,\where\, f(x)={1-2x ,xlt=0 ;1+2x ,xgt=0} , (ii)\ int_(-1)^4f(x)dx ,\where\, f(x)={2x+8,-1lt=xlt=2; 6x, 2lt=xlt=4}

Calculate lim_(x to 2) , where f(x) = {{:(3 if ,x le 2),(4 if, x gt 2):}

If f(x)={:{(3x^2+12x-1"," -1le x le2),(37-x ","2 lt x le 3):} then

Let f(x) be defined in the interval [0,4] such that f(x) ={{:(1-x,0lex le 1),( x+2, 1lt xlt2),( 4-x, 2 le x le 4):} , then the number of points where f(x) is discontinuous is (a) 1 (b) 2 (c) 3 (d) none of these

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

A function f is defined on the set of real numbers as follows: f(x)={(x+1, 1 le x lt 2),(2x-1, 2 le x lt 4), (3x-10, 4 le x lt 6):} (a) Find the domain of the function. (b) Find the range of the function.