Answer to Question #120168 in Calculus for Emily

Question

Determine the area of the region bounded by f(x) = 2x
2 + 10 and g(x) = 4x + 1

Answer 1

IAs per the given function f(x) = 2x

2 + 10 and g(x) = 4x + 1,

f(x) actually means 4x + 10

In that case f(x) and g(x) represent two parallel straight lines and hence enclose no area.

If f(x) is considered as 2x²+10 and g(x) = 4x + 1 , then no area is bounded by them.

Graph is attached.

But if the function f(x) be considered as f(x) = 2x²+1 and g(x) = 4x+1 then there is a bounded area.

Graph is attached

And area = $\int_{0}^{2} [g(x) - f(x)] dx$

= $\int_{0}^{2} [4x + 1 - 2x²-1] dx$

= $\int_{0}^{2} [4x - 2x²] dx$

= [ 4x²/2 - 2x³/3]₀²

= 8 - 16/3 square unit

= 8/3 square unit

= 2.67 square unit