Question

The are bounded by the curve $y=f\left(x\right)$ and the lines $x=0,y=0$ and $x=t$, lies in the interval

• A. $(\frac{21}{64},\frac{11}{16})$
• B. $(\frac{3}{4},3)$
• C. $(9,10)$
• D. $(0,\frac{21}{64})$

Answer 1

The correct option is B $(\frac{3}{4},3)$

${\int }_0^{\frac{1}{2}}f\left(x\right)dx<{\int }_0^{t}f\left(x\right)dx<{\int }_0^{\frac{3}{4}}f\left(x\right)dx$
$\int f\left(x\right)dx=x+x^2+x^3+x^4$

${\int }_0^{\frac{1}{2}}f\left(x\right)dx=\frac{13}{16}>\frac{3}{4}$
${\int }_0^{\frac{3}{4}}f\left(x\right)dx=\frac{525}{256}<3$