Q. The slope of tangent to a curve $y = f(x)$ at $(x,\ f(x))$ is $2x + 1$. If the curve passes through the point (1, 2), then the area of the region bounded by the curve, the $x$-axis and the line $x = 1$ is
A) $\frac{5}{6}$ sq unit
B) $\frac{6}{5}$ sq unit
C) $\frac{1}{6}$ sq unit
D) 6 sq unit
Explanation
(a)
We have, $\frac{dy}{dx} = 2x + 1$
$\Rightarrow \ y = x^{2} + x + c$, it passes through (1, 2)
$\therefore\ c = 0$
Then, $y = x^{2} + x$
$\therefore$ Required area $= \int_{0}^{1}{\left( x^{2} + x \right)dx = \frac{5}{6}}\ sq\ unit$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.