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Approximating the Area Under a Curve- HW Problems
1. Approximate the area under the graph of 𝑓 (𝑥 ) = sin(𝑥 ) from
𝑥 = 0 to 𝑥 = 𝜋 using
a. Right endpoints and 𝑛 = 4
b. Right endpoints and 𝑛 = 8
c. Left endpoints and 𝑛 = 4
d. Left endpoints and 𝑛 = 8.
2. Approximate the area under the graph of 𝑓 (𝑥 ) = 4 − 𝑥 2 from
𝑥 = −2 to 𝑥 = 2 using 𝑛 = 4 and
a. Left endpoints
b. Midpoints
c. Right endpoints.
3. Approximate the area under the graph of 𝑓 (𝑥 ) = √𝑥 from
𝑥 = 1 to 𝑥 = 4 using 𝑛 = 3 and
a. Left endpoints
b. Midpoints
c. Right endpoints.
Approximating the Area Under a Curve- HW Problems
1. Approximate the area under the graph of 𝑓 (𝑥 ) = sin(𝑥 ) from
𝑥 = 0 to 𝑥 = 𝜋 using
a. Right endpoints and 𝑛 = 4
b. Right endpoints and 𝑛 = 8
c. Left endpoints and 𝑛 = 4
d. Left endpoints and 𝑛 = 8.
2. Approximate the area under the graph of 𝑓 (𝑥 ) = 4 − 𝑥 2 from
𝑥 = −2 to 𝑥 = 2 using 𝑛 = 4 and
a. Left endpoints
b. Midpoints
c. Right endpoints.
3. Approximate the area under the graph of 𝑓 (𝑥 ) = √𝑥 from
𝑥 = 1 to 𝑥 = 4 using 𝑛 = 3 and
a. Left endpoints
b. Midpoints
c. Right endpoints.
