Find the area below the curve y = (x - 5 )^2 above the x-axis and between the vertical lines x=-3 and x=4.?

Answer 1

4
∫(x - 5)^2 dx =
-3
4
∫[x^2 - 10x + 25] dx =
-3
(1/3)x^3 - 5x^2 + 25x from - 3 to 4 =
(1/3)(4^3 - (- 3)^3) - 5(4^2 - (- 3)^2) + 25(4 - (-3)) =
(1/3)(64 + 27) - 5(16 - 9) + 25(4 + 3) =
21 + 1/3 + 9 - 80 + 45 + 100 + 75 =
170 1/3 ≈ 170.33

Answer 2

integrate x^2-10x+25 and solve from x =-3 to x = 4

170.333