Practicing Success
The slope of the tangent to a curve y = f(x) at [x, f(x)] is 2x + 1. If the curve passes through the point (1, 2), then area bounded by the curve, x-axis and the line x = 1 is |
$\frac{5}{6}$ $\frac{6}{5}$ $\frac{1}{6}$ 6 |
$\frac{5}{6}$ |
$\frac{d y}{d x}=2 x+1 \Rightarrow y=x^2+x+c$ It passes through (1, 2) ∴ c = 0 ∴ $y+\frac{1}{4}=\left(x+\frac{1}{2}\right)^2$ It is a parabola with vertex $\left(-\frac{1}{2},-\frac{1}{4}\right)$ ∴ Required area $=\int\limits_0^1 y d x=\int\limits_0^1\left(x^2+x\right) d x=\frac{5}{6}$. Hence (1) is the correct answer. |