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

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: (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}

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

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

Let f(x)= {{:(1+ sin x, x lt 0 ),(x^2-x+1, x ge 0 ):}

Evaluate: int_0^4 1/(x+sqrt(x))dx (ii) int_0^1(2x)/(5x^2+1)dx

if f(x) ={{:( x-1, xlt 0),( x^(2) - 2x , x ge 0):} , then

If f(x) is defined as f(x)={{:(2x+3,x,le 0),(3x+3,x,ge 0):} then evaluate : lim_(xrarr0) f(x) "and" lim_(xrarr1) f(x)

Let f_(1) : R to R, f_(2) : [0, oo) to R, f_(3) : R to R be three function defined as f_(1)(x) = {(|x|, x < 0),(e^x , x ge 0):}, f_(2)(x)=x^2, f_(3)(x) = {(f_(2)(f_1(x)),x < 0),(f_(2)(f_1(x))-1, x ge 0):} then f_3(x) is: