Find the area bounded by the two curves and the given pair of lines. y=x² + 3, y= x + 1, x=-1, x=0

Answer 1

integral of x^2 + 3= x^3/3 + 3x

evaluated at x= -1 to x=0 is 1/3 +3 = 10/3

integral of x+1 = x^2/2 +x

evaluated at x= -1 to x = 0 is -1/2 +1 = 1/2

10/3 -1/2 = 20/6 -3/6 = 17/6

you might try graphing the parabola and line

the area between the two is a triangle plus a square plus the area under x^2 and the x axis from x = 0 to 1

or 2 + 1/2 + 1/3 = 17/6

Answer 2

f(x) = x²+3 g(x) = x+1

Area, A = ∫_-1⁰ x²+3-x-1 dx = x³/3-x²/2+2x|_-1⁰

A = 0 -0 +0 -(-1/3-1/2-2) = 2/6 + 3/6 + 12/6 = 17/6