Using rectangles, estimate the area under the parabola y = x2 from 0 t | Mathematics I 2078

Mathematics I207810 marksNumerical: Riemann sum and particle motionRectilinear motion

Using rectangles, estimate the area under the parabola $y = x^2$ from 0 to 1. A particle moves along a line so that its velocity v at time t is $v = t^2 + t + 6$ . (i) find the displacement of the particle during the time period $1 \leq t \leq 4$ . (ii) find the distance traveled during this time period. [5+5+0]

Using rectangles, estimate the area under the parabola $y = x^2$ from 0 to 1. A particle moves along a line so that its velocity v at time t is $v = t^2 + t + 6$. (i) find the displacement of the particle during the time period $1 \leq t \leq 4$. (ii) find the distance traveled during this time period. [5+5+0]

Curve: $y = x^2$ , interval $[0,1]$ . - Velocity: $v(t) = t^2 + t + 6$ , time interval $1 \le t \le 4$ . --- (a) Area under $y=x^2$ from 0 to 1 (rectangle method) Divide $[0,1]$ into $n$ equal subintervals. - Width: $\Delta x = \dfrac{1}{n}$ - Right endpoints: $xi = \dfrac{i}{n}$ - Height:

Curve: $y = x^2$, interval $[0,1]$. - Velocity: $v(t) = t^2 + t + 6$, time interval $1 \le t \le 4$. --- (a) Area under $y=x^2$ from 0 to 1 (rectangle method) Divide $[0,1]$ into $n$ equal subintervals. - Width: $\Delta x = \dfrac{1}{n}$ - Right endpoints: $xi = \dfrac{i}{n}$ - Height:

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