question 1 (1 point)\ncompute the approximating sum to the area under the graph of\nf(x)=5x - x^{2}\non the…

question 1 (1 point)\ncompute the approximating sum to the area under the graph of\nf(x)=5x - x^{2}\non the interval (0,2) using (n = 4) and left endpoints.\nchoose the correct answer from the following.\n6.75\n7.75\n6.25\n5.75\n7.25

question 1 (1 point)\ncompute the approximating sum to the area under the graph of\nf(x)=5x - x^{2}\non the interval (0,2) using (n = 4) and left endpoints.\nchoose the correct answer from the following.\n6.75\n7.75\n6.25\n5.75\n7.25

Answer

Explanation:

Step1: Calculate $\Delta x$

$\Delta x=\frac{2 - 0}{4}=0.5$

Step2: Find left - endpoints

$x_0 = 0,x_1=0.5,x_2 = 1,x_3=1.5$

Step3: Calculate sum

$S=\sum_{i = 0}^{3}f(x_i)\Delta x=0.5\times(f(0)+f(0.5)+f(1)+f(1.5))$ $=0.5\times(0 + 2.25+4+5.25)=6.75$

Answer:

6.75