Question

Find the area enclosed between the curve y = x2 + 2, X-axis, x = 3 and x = 4

Answer 1

The area region enclosed by the curves $y=x^2+2$ , x-axis and x=4 is given by

$area= ∫_3^4ydx=∫_3^4(x^2+2)dx$

$=[x^3/3+2x]_3^4$

$=[4^3/3+2(4)]-[3^3/3+2(4)]$

$=88/3-15$

=14.333 square units of length