`int_(2)^(8)f(x)dx` where `f(x)={:{(3x+4",",2lexle3),(x^(2)+4",",3lexle8):}`.

Evaluate int_(1)^(4)f(x)dx , where f(x)={:{(2x+8",",1lexle2),(6x",",2lexle4):} .

int_(1)^(4)f(x)dx where f(x)={:{(4x+3",",1lexle2),(3x+5",",2lexle4):}

Evaluate int_(0)^(3)f(x)dx , where f(x)={:{(x+3,0lexle2),(3x" ",2lexle3):}

f(x)={{:(x^(2)", "xle2),(8-2x", "2ltxlt4),(4", "xge4):}

int(2^(8x+3))/(2^(4x+3))dx:

If f(x)={{:(x",",0lexle1),(2-e^(x-1)",",1ltxle2),(x-e",",2ltxle3):} and g'(x)=f(x), x in [1,3] , then

Consider two function y=f(x) and y=g(x) defined as f(x)={{:(ax^(2)+b,,0lexle1),(bx+2b,,1ltxle3),((a-1)x+2c-3,,3ltxle4):} and" "g(x)={{:(cx+d,,0lexle2),(ax+3-c,,2ltxlt3),(x^(2)+b+1,,3gexle4):} lim_(xrarr2) (f(x))/(|g(x)|+1) exists and f is differentiable at x = 1. The value of limit will be

Consider two function y=f(x) and y=g(x) defined as f(x)={{:(ax^(2)+b,,0lexle1),(bx+2b,,1ltxle3),((a-1)x+2c-3,,3ltxle4):} and" "g(x)={{:(cx+d,,0lexle2),(ax+3-c,,2ltxlt3),(x^(2)+b+1,,3gexle4):} Let f be differentiable at x = 1 and g(x) be continuous at x = 3. If the roots of the quadratic equation x^(2)+(a+b+c)alphax+49(k+kalpha)=0 are real distinct for all values of alpha then possible values of k will be

If the function f : R to R is defined by f(x)={{:(2x+7","x lt -2),(x^(2)-2","-2 le x lt 3","),(3x-2","x ge 3):} then find the values of (i) f(4) (ii) f(-2) (iii) f(4)+2f(1) (iv) (f(1)-3f(4))/(f(-3))