Find the area of the region bounded by y = x2 and y = 2x - x2. Using t | Mathematics I 2078

Mathematics I207810 marksNumerical: Area between curves and trapezoidal ruleAreas between the curves

Find the area of the region bounded by $y = x^2$ and $y = 2x - x^2$ .

Using trapezoidal rule, approximate $\int_1^2 \frac{1}{x} dx$ with $n=5$ .

[5+5]

Find the area of the region bounded by $y = x^2$ and $y = 2x - x^2$.

Using trapezoidal rule, approximate $\int_1^2 \frac{1}{x} dx$ with $n=5$.

[5+5]

Curves: $y = x^2$ and $y = 2x - x^2$ - Integral: $\int1^2 \frac{1}{x}\,dx$ , $n = 5$ --- $x^2 = 2x - x^2 \implies 2x^2 - 2x = 0 \implies 2x(x-1) = 0$ $x = 0 \quad \text{or} \quad x = 1$ At $x = 0.5$ : - $y = x^2 = 0.25$ - $y = 2x - x^2 = 0.75$ So $y = 2x - x^2$ is above $y = x^2$ on $[0,1]$ . ...

Curves: $y = x^2$ and $y = 2x - x^2$ - Integral: $\int1^2 \frac{1}{x},dx$, $n = 5$ --- $$x^2 = 2x - x^2 \implies 2x^2 - 2x = 0 \implies 2x(x-1) = 0$$ $$x = 0 \quad \text{or} \quad x = 1$$ At $x = 0.5$: - $y = x^2 = 0.25$ - $y = 2x - x^2 = 0.75$ So $y = 2x - x^2$ is above $y = x^2$ on $[0,1]$. ...

Find the area of the region bounded by y = x2 and y = 2x - x2. Using trapezoidal rule, approximate int12 frac1x dx with n=5. [5+5]