The slope to the 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 y = f(x), the x-axis and the line x = 1 is
Answer & explanation
Correct answer: option 1
We are given that $\frac{dy}{dx}=2x+1$
⇒ y = x2 + x + c, and since the curve passes through the point (1, 2), c = 0.
Hence the curve is y = x2 + x (see the figure); the required area $=\int\limits_0^1y\,dx=\int\limits_0^1(x^2+x)dx=\frac{5}{5}$.
Hence (A) is the correct answer.