Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
$g(x)=\left\{\begin{array}{ccc}0 & \text { if } & x < a, \\ \int_a^x f(t) d t & \text { if } & a \leq x \leq b, \\ \int_a^b f(t) d t & \text { if } & x > b .\end{array}\right.$, Then
$(A)$ $g(x)$ is continuous but not differentiable at a
$(B)$ $g(x)$ is differentiable on $R$
$(C)$ $g(x)$ is continuous but not differentiable at $b$
$(D)$ $g(x)$ is continuous and differentiable at either a or $b$ but not both
$\int_0^1 {(1 + {{\cos }^8}x)(a{x^2} + bx + c)\,dx} = \int_0^2 {(1 + {{\cos }^8}x)(a{x^2} + bx + c)\,dx} $
Then the quadratic equation $a{x^2} + bx + c = 0$ has