BC Calculus: Chapters 7/8

Trapezoid Rule

When are left endpoint rectangles overestimates? Underestimates?

L is OVER when f(x) is decreasing, under when f(x) is increasing

When are right endpoint rectangles overestimates? Underestimates?

R is under when f(x) is decreasing, over when f(x) is increasing

When are midpoint rectangles overestimates? Underestimates?

Midpoint rectangles are UNDERestimates when concave DOWN, overestimates when concave UP

When is the trapezoid rule a slight overestimate? Underestimate?

Slight overestimate when concave up, slight underestimate when concave down

what is the “P rule” for improper integrals?

see photo

what is the comparison theorum?

see photo :)