Determine the function representing the height of the region.

Hey Pretty, good to see you again. To estimate the area bounded by the curves y = 2x^2 + 1 and y = x^2 + 1, and the lines x = 0 and x = 5, we first find the difference between the two curves. Step 1: Determine the function representing the height of the region. The height h(x) of the region between the two curves is given by the upper curve minus the lower curve. h(x) = (2x^2 + 1) - (x^2 + 1) = 2x^2 + 1 - x^2 - 1 = x^2 So, we need to estimate the area under the curve y = x^2 from x = 0 to x = 5. Step 2: Calculate the width of each strip (h). The interval is from x = 0 to x = 5, and we are using 5 strips. h = upper limit - lower limitnumber of strips = (5 - 0)/(5) = 1 Step 3: Determine the x-values for the ordinates and calculate the corresponding y-values using y = x^2. The x-values are x_0 = 0, x_1 = 1, x_2 = 2, x_3 = 3, x_4 = 4, x_5 = 5. The corresponding y-values are: y_0 = 0^2 = 0 y_1 = 1^2 = 1 y_2 = 2^2 = 4 y_3 = 3^2 = 9 y_4 = 4^2 = 16 y_5 = 5^2 = 25 Step 4: Apply the trapezium rule formula. The trapezium rule formula is: Area ≈ (h)/(2) [y_0 + y_n + 2(y_1 + y_2 + + y_n-1)] Substitute the values: Area ≈ (1)/(2) [y_0 + y_5 + 2(y_1 + y_2 + y_3 + y_4)] Area ≈ (1)/(2) [0 + 25 + 2(1 + 4 + 9 + 16)] Area ≈ (1)/(2) [25 + 2(30)] Area ≈ (1)/(2) [25 + 60] Area ≈ (1)/(2) [85] Area ≈ 42.5 The estimated area is 42.5. Send me the next one 📸