Find the area of the region between the x-axis and the graph of f(x) = | Basic Mathematics 2079

Basic Mathematics20795 marksNumerical: area under curveArea under curves

Find the area of the region between the x-axis and the graph of $f(x) = x^3 - x^2 - 2x$ , $1 \leq x \leq 2$ . [5]

Find the area of the region between the x-axis and the graph of $f(x) = x^3 - x^2 - 2x$, $1 \leq x \leq 2$. [5]

Function: $f(x) = x^3 - x^2 - 2x$ - Interval: $1 \leq x \leq 2$ - Find area between curve and x-axis. Step 1: Zeros of f(x) $f(x) = x(x^2 - x - 2) = x(x-2)(x+1)$ Zeros: $x = 0, 2, -1$ . In $[1,2]$ the only zero is $x = 2$ (endpoint). Step 2: Sign of f(x) on [1,2] At $x = 1.5$ : $$f(1.5) = 3.375...

Function: $f(x) = x^3 - x^2 - 2x$ - Interval: $1 \leq x \leq 2$ - Find area between curve and x-axis. Step 1: Zeros of f(x) $$f(x) = x(x^2 - x - 2) = x(x-2)(x+1)$$ Zeros: $x = 0, 2, -1$. In $[1,2]$ the only zero is $x = 2$ (endpoint). Step 2: Sign of f(x) on [1,2] At $x = 1.5$: $$f(1.5) = 3.375...

Find the area of the region between the x-axis and the graph of f(x) = x3 - x2 - 2x, 1 leq x leq 2.