area between curves that intersect at more than two points (calculator - active)\ngoogle classroom\nmicrosoft…
area between curves that intersect at more than two points (calculator - active)\ngoogle classroom\nmicrosoft teams\nlet f(x)=1/2x³ - 2x + 3 and g(x)=x² + 7/2x - 3.\nfind the sum of the areas enclosed by the graphs of f and g between x = - 3 and x = 4.\nuse a graphing calculator and round your answer to three decimal places.\n57.083
Answer
Explanation:
Step1: Find intersection points
Set $f(x)=g(x)$, so $\frac{1}{2}x^{3}-2x + 3=x^{2}+\frac{7}{2}x - 3$. Rearrange to $\frac{1}{2}x^{3}-x^{2}-\frac{11}{2}x + 6 = 0$. Using a graphing - calculator to find the intersection points in the interval $[-3,4]$.
Step2: Set up integral for area
The area $A=\int_{a}^{b}|f(x)-g(x)|dx$. We need to split the integral based on the intersection points in $[-3,4]$. Let $h(x)=f(x)-g(x)=\frac{1}{2}x^{3}-x^{2}-\frac{11}{2}x + 6$.
Step3: Evaluate integral with calculator
Use a graphing calculator to evaluate $\int_{-3}^{4}| \frac{1}{2}x^{3}-x^{2}-\frac{11}{2}x + 6|dx$.
Answer:
$57.083$