Question

If f(x)=3x^3 then what is the area enclosed by the graph of the function, the horizontal axis, and vertical lines at x=2 and x=4

Answer 1

Area: 180 units2 (units 2 is because since the are no specific unit given but every area should have a unit of measurement)

Explanation:

The area enclosed by the graph of the function, the horizontal axis, and vertical lines is the integral of the function between thos two points (x=2 and x=4)

So , let's solve the integral of f(x)

Area =
`\int\limits^2_4 3{x}^3 \, dx = 3*x^4/4`+C

C=0

So if we evaluate this function in the given segment:

Area= 3* (4^4)/4-3*(2^4)/4= 3*(4^4-2^4)/4=180 units 2

Goos luck!