Question

Write the summation to estimate the area under the curve y = 2x2 + 1 from x = 0 to x = 4 using 4 rectangles and left endpoints.

the summation from i equals 0 to 4 of the quantity 2 times i squared plus 1
the summation from i equals 1 to 3 of the quantity 2 times i squared plus 1
the summation from i equals 0 to 3 of the quantity 2 times i squared plus 1
the summation from i equals 1 to 4 of the quantity 2 times i squared plus 1

Answer 1

Hello,
Answer C:
the summation from i equals 0 to 3 of the quantity 2 times i squared plus 1
$\sum_{i=0}^3[(i+1-i)*(2*i^2+1)]\\\\ =\sum_{i=0}^3[(2*i^2+1)]$

Answer 2

Answer:

The correct option is C.

Step-by-step explanation:

The given equation of curve is

$y=2x^2+1$

We need to find the area under the given curve from x = 0 to x = 4 using 4 rectangles and left endpoints.

We have 4 rectangles in x = 0 to x = 4. So,

$\Delta x=1$

Left Riemann sum:

$\sum_{i=0}^{n-1}\Delta xf(x_i)$

Using Left Riemann sum, we get

$\sum_{i=0}^{4-1}(1)f(i)$

$\sum_{i=0}^{3}(2i^2+1)$             $[\because y=2x^2+1]$

The area under the given curve from x = 0 to x = 4 using 4 rectangles and left endpoints is

$\sum_{i=0}^{3}2i^2+1$

Therefore the correct option is C.