Difference between revisions of "009B Sample Midterm 1, Problem 5"

Revision as of 18:44, 19 January 2016

Let $f(x)=1-x^{2}$ .

a) Compute the left-hand Riemann sum approximation of

\int _{0}^{3}f(x)dx

with

n=3

boxes.

b) Compute the right-hand Riemann sum approximation of

\int _{0}^{3}f(x)dx

with

n=3

boxes.

c) Express

\int _{0}^{3}f(x)dx

as a limit of right-hand Riemann sums (as in the definition of the definite integral). Do not evaluate the limit.

Solution:

Final Answer:

@@ Line 1: / Line 1: @@
-<span class="exam">Divide the interval <math>[0,\pi]</math> into four subintervals of equal length <math>\frac{\pi}{4}</math> and compute the right-endpoint Riemann sum of <math>y=\sin (x)</math>
+<span class="exam">Let <math>f(x)=1-x^2</math>.
+::<span class="exam">a) Compute the left-hand Riemann sum approximation of <math>\int_0^3 f(x)dx</math> with <math>n=3</math> boxes.
+::<span class="exam">b) Compute the right-hand Riemann sum approximation of <math>\int_0^3 f(x)dx</math> with <math>n=3</math> boxes.
+::<span class="exam">c) Express <math>\int_0^3 f(x)dx</math> as a limit of right-hand Riemann sums (as in the definition of the definite integral). Do not evaluate the limit.