77
Chapter 9: Areas and Riemann Sums
Using Limits and Riemann
Sums to Find Expressions
for Definite Integrals
531–535 Find an expression for the definite integral
using the definition. Do not evaluate.
531.
x dx
1
4
∫
532.
sin
2
0
x dx
π
∫
533.
x
x dx
2
1
5
+
(
)
∫
534.
tan
sec
/
x
x dx
+
(
)
∫ 0
4
π
535.
3
5
3
2
4
6
x
x
x
dx
+
− +
(
)
∫
Calculating Riemann Sums
Using Midpoints
527–530 Find the Riemann sum for the given
function with the specified number of intervals
using midpoints.
527. f
 
(x) = 2 cos x, 0 ≤ x ≤ 3, n = 4. Round your
answer to two decimal places.
528. f x
x
x
( ) sin
= + 1
, 1 ≤ x ≤ 5, n = 5. Round your
answer to two decimal places.
529. f
 
(x) = 3e
x
+ 2, 1 ≤ x ≤ 4, n = 6. Round your
answer to two decimal places.
530. f x
x x
( ) =
+ , 1 ≤ x ≤ 5, n = 8. Round your
answer to two decimal places.