Question

In this problem, we will practice setting up a Riemann sum to approximate the area between g(x) = sin(x) and the x-axis over [0, ?] using n rectangles. First, if we divide [0, ?] into n subintervals of equal width, what is the width ?x of each of these subintervals? ?x = What is the right endpoint $r_i$ of subinterval i, where 1 ? i ? n? $r_i$ = What is the height of the $i^{th}$ rectangle if we use the right endpoint of the $i^{th}$ subinterval, $r_i$, to compute its height? Height of Rectangle i: What is the area of the $i^{th}$ rectangle? Area of Rectangle i: Let's try out our previous formula. If use 200 rectangles in our area approximation, what would be the area of rectangle 112 ? Round your answer to 4 decimal places. Area of Rectangle 112 out of 200: Using the summation capabilities of your calculator, find the area approximation given by 200 rectangles. Round your answer to 6 decimal places. $\int_0^\pi \sin(x) dx \approx \sum_{i=1}^n g(r_i) \Delta x = $

          In this problem, we will practice setting up a Riemann sum to approximate the area between
g(x) = sin(x) and the x-axis over [0, ?] using n rectangles.
First, if we divide [0, ?] into n subintervals of equal width, what is the width ?x of each of these
subintervals?
?x =
What is the right endpoint $r_i$ of subinterval i, where 1 ? i ? n?
$r_i$ =
What is the height of the $i^{th}$ rectangle if we use the right endpoint of the $i^{th}$ subinterval, $r_i$, to compute
its height?
Height of Rectangle i:
What is the area of the $i^{th}$ rectangle?
Area of Rectangle i:
Let's try out our previous formula. If use 200 rectangles in our area approximation, what would be the area
of rectangle 112 ? Round your answer to 4 decimal places.
Area of Rectangle 112 out of 200:
Using the summation capabilities of your calculator, find the area approximation given by 200 rectangles.
Round your answer to 6 decimal places.
$\int_0^\pi \sin(x) dx \approx \sum_{i=1}^n g(r_i) \Delta x = $

In this problem, we will practice setting up a Riemann sum to approximate the area between
g(x) = sin(x) and the x-axis over [0, ?] using n rectangles.
First, if we divide [0, ?] into n subintervals of equal width, what is the width ?x of each of these
subintervals?
?x =
What is the right endpoint ri of subinterval i, where 1 ? i ? n?
ri =
What is the height of the i^th rectangle if we use the right endpoint of the i^th subinterval, ri, to compute
its height?
Height of Rectangle i:
What is the area of the i^th rectangle?
Area of Rectangle i:
Let's try out our previous formula. If use 200 rectangles in our area approximation, what would be the area
of rectangle 112 ? Round your answer to 4 decimal places.
Area of Rectangle 112 out of 200:
Using the summation capabilities of your calculator, find the area approximation given by 200 rectangles.
Round your answer to 6 decimal places.
∫0^πsin(x) dx ≈∑i=1^n g(ri) Δ x =

Added by Gabrielle B.

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