MWFsolnt1-sp08

# MWFsolnt1-sp08 - TEST 1 SOLUTIONS (MWF version) MATH 1042...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: TEST 1 SOLUTIONS (MWF version) MATH 1042 SPRING 2008 1. Since n X k =1 1 2 c k + 1 x k is a Riemann sum, lim k P k n X k =1 1 2 c k + 1 x k is a definite integral. Since the sum is defined on the interval [0 , 4], the limit is 4 Z 1 2 x + 1 dx . To evaluate this integral, let u = 2 x +1. Then du = 2 dx , and the integral becomes 1 2 R 9 1 1 u du = 1 2 R 9 1 u- 1 2 du = 1 2 2 u 1 2 9 1 = u 9 1 = 3- 1 = 2. 2. The graph of a function f consists of a semicircle and line segments. K 2 2 3 4 K 1 2 Note that the radius of the semicircle is 2, so the area of the semicircle is 1 2 4 = 2 . Similarly, the area of the triangular region is 1 2 1 1 = 1 2 , and the area of the rectangle over the horizontal line segment is 1 1 = 1. Since g ( x ) = R x- 2 f ( t ) dt , (a) g (- 2) = R- 2- 2 f ( t ) dt = 0, since the upper and lower limits of integration are equal. (b) g (2) = R 2- 2 f ( t ) dt = 2 . (c) g (4) = R 4- 2 f ( t ) dt = R- 2- 2 f ( t ) dt + R 4 2 f ( t ) dt = 2 - 1 2- 1 = 2 - 3 2 ....
View Full Document

## This homework help was uploaded on 04/18/2008 for the course MATH 1042 taught by Professor Dr.z during the Spring '08 term at Temple.

### Page1 / 4

MWFsolnt1-sp08 - TEST 1 SOLUTIONS (MWF version) MATH 1042...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online