Question

Use limits to find the area of the region between the graph of y=x³+1

and the x-axis on the interval [2, 4], or f(x³ + 1) dx

Answer 1

62

Step-by-step explanation:

Find the area of the region bounded the graph of y=x³+1 and the x-axis over the interval [2,4].

`\text{\underline{Set up:}}\\\\\Longrightarrow \boxed{\int\limits^4_2 {x^3+1} \, dx}`

`\text{Now solving...}\\\\\Longrightarrow \int\limits^4_2 {x^3+1} \, dx\\\\\Longrightarrow (1)/(4)x^4+x \Big]\limits^4_2\\\\\Longrightarrow [(1)/(4)(4)^4+(4)]-[(1)/(4)(2)^4+(2)]\\\\\Longrightarrow [68]-[6]\\\\\Longrightarrow \boxed{\boxed{=62}}`

Thus, the problem is solved.