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 bounded by the curve, x - axis and line x = 1 is :
Answer & explanation
Correct answer: option 1
\(\frac{dy}{dx} = 2x + 1\)
⇒ ∫dy = ∫(2x + 1) dx
y = x2 + x + c
It passes through (1,2) ⇒ c = 0, then curve is y = x2 + x
The area bounded by y = x2 + x, x - axis and line x = 1 is :
\(\int_{0}^{1} [x^2 + x] dx = \frac{5}{6}\)