Answer:
62
Explanation:
Find the area of the region bounded the graph of y=x³+1 and the x-axis over the interval [2,4].
[tex]\text{\underline{Set up:}}\\\\\Longrightarrow \boxed{\int\limits^4_2 {x^3+1} \, dx}[/tex]
[tex]\text{Now solving...}\\\\\Longrightarrow \int\limits^4_2 {x^3+1} \, dx\\\\\Longrightarrow \frac{1}{4}x^4+x \Big]\limits^4_2\\\\\Longrightarrow [\frac{1}{4}(4)^4+(4)]-[\frac{1}{4}(2)^4+(2)]\\\\\Longrightarrow [68]-[6]\\\\\Longrightarrow \boxed{\boxed{=62}}[/tex]
Thus, the problem is solved.
