Question

The slope of tangent to the curve $y=f(x)$ at $(x, f(x))$ is $(2 x+1)$. If the curve passes through the point $(1,2)$, then the area bounded by the curve the $x$-axis and line $x=1$ is

• A. $\frac{5}{6}$
• B. $\frac{6}{5}$
• C. $\frac{1}{6}$
• D. 6

Answer 1

Answer: (A)

$\frac{ dy }{ dx }=2 x +1$
$y=x^2+x+C $
$2=2+C \Rightarrow C=0 $
$y=x^2+x$
$\text { Area }=\int\limits_0^1\left(x^2+x\right) d x=\frac{1}{3}+\frac{1}{2}=\frac{5}{6} .$