wk1quiz

# wk1quiz - f x = x 3 x is odd By a property of the deﬁnite...

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

Name: Score: 10B Practice Quiz Please return during Monday’s lecture. You may use whatever resources you like. 1. (5) Approximate the distance, given the following time vs. velocity table. Use n = 3 left endpoint rectangles. t 0 2 4 6 8 10 12 v ( t ) 10 15 17 21 30 32 15 Solution: If we use 3 left endpoint rectangles, then Δ t = b - a 3 = 12 3 = 4 This means our lefthand sum is equal to L ( f ) = 2 X i =0 v ( a + i Δ t t = v ( a t + v ( a + Δ t t + v ( a + 2Δ t t Substituting our values in, we get L ( f ) = 4 v (0) + 4 v (4) + 4 v (8) = 4(10 + 17 + 30) = 228 So the answer is 228 units 2 2. (5) Compute the following deﬁnite integral using the fundamental theorem of calculus. Z 1 - 1 ( x 3 + x ) dx Solution: The key thing is that the integrand,

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: f ( x ) = x 3 + x is odd. By a property of the deﬁnite integral, Z 1-1 ( x 3 + x ) dx = 0 3. (5) Write down, but do not evaluate, an expression for the right hand Riemann sum with n = 100 that approximates Z 2-1 sin( x ) e x dx Solution: Again, the general formula for the righthand Riemann sum is R ( f ) = n-1 X i =1 f ( a + i Δ x )Δ x In our case, a =-1 and n = 100. This means Δ x = b-a n = 2-(-1) 100 = 3 / 100 Now we can simply plug in our values, obtaining Z 2-1 sin( x ) e x dx ≈ L ( f ) = 99 X i =1 sin(-1 + i Δ x ) e-1+ i Δ x Δ x...
View Full Document

## This note was uploaded on 09/13/2010 for the course MATH math 10b taught by Professor Reed during the Summer '10 term at UCSD.

### Page1 / 2

wk1quiz - f x = x 3 x is odd By a property of the deﬁnite...

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

View Full Document
Ask a homework question - tutors are online