Find the area of the region bounded by the graphs y=-x^2+3x+4 and y=4

Answer 1

Area under the curve = integral

Our region is [y = -x^2+3x+4] - [y = 4].

Then the area is integral of above expression which is equivalent to -x^2+3x.

Now, to find the definite integral, we need lower and upper bound which can be found by setting two equations to each other, giving you x = 0 to x = 3.

Hence, A(x) = integral (x = 0 to x = 3) [-x^2 + 3x] dx = 4.5

Answer 2