Question

6. Approximate the area under the curve of y = -x2 + 12 over the interval [-2, 2) using 4 left endpoint rectangles.

Answer 1

Soln Given curve y = -x ² +12 ,n=4, a = -2, 6=2 to approximate the area under the curve, we can circum & cribe the wire wore using rectangle follows. We divide the interval [-2, 2] into 4 Aubintervals of equal lenght Ax=b-a2 Ax=2-(-2) 4 Ax=1 We divide the integral [-2, 2] into n=4 subinterval of length sx=1 1 ) Y x₃ = 1 1 we label the end points of these subintervals to = -2, x,-1, X2-0 Now, we jupt evaluate the function at the left and points f(x) = -(-2) + 12 = 8 f(x) = f(-1) = -(-1) 7 1 2 = f(x) = f(0) = -(0)² + 12 = 12 - 2 D -(1+1211 f (x) = f(1) =

N areas We use the sum the of approximating rectangles to approximate the area under the cure, we get 4 is 1 AS LA [ f(x2-1)ax = f(x) sx + f(x).ax + f(x). ax + f(x3):48 {<a = left and approximation ? Inserting the values 1 24 = 8.(1) + 11() + 12 (1) +11(1) 24 8 + 11 + 12 +11 La 42 my