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)={(2x+8,1lex,le,2),(6x,2lex,le,4):}

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: int1/(x^4+3x^2+1)\ dx

Evaluate: int1/(1+x+x^2+x^3)dx

Evaluate: int1/(1+x+x^2+x^3)dx

Evaluate: intf(x)/(x^3-1)dx , where f(x) is a polynomial of degree 2 in x such that f(0)=f(1)=3f(2)=-3

Evaluate: int_(-1)^4f(x)dx=4a n dint_2^4(3-f(x))dx=7, then find the value of int_2^(-1)f(x)dxdot

Evaluate: int_(-1)^4f(x)dx=4a n dint_2^4(3-f(x))dx=7, then find the value of int_-1^(2)f(x)dxdot

The value of int_1^2 {f(g(x))}^(-1)f'(g(x))g'(x) dx , where g(1)=g(2), is equal to

Find number of roots of f(x) where f(x) = 1/(x+1)^3 -3x + sin x