×

### Let's log you in.

or

Don't have a StudySoup account? Create one here!

×

or

## Calculus II: Week One notes

by: Alison Holden

28

4

4

# Calculus II: Week One notes M 145

Marketplace > University of Hartford > M 145 > Calculus II Week One notes
Alison Holden
University of Hartford

Enter your email below and we will instantly email you these Notes for Calculus II

(Limited time offer)

Unlock FREE Class Notes

Everyone needs better class notes. Enter your email and we will send you notes for this class for free.

This includes u-substitution, particle motion, difference between distance, and displacement, and integral rules. Will be on exam 1.
COURSE
Calculus II
PROF.
TYPE
Class Notes
PAGES
4
WORDS
CONCEPTS
Calculus
KARMA
Free

## Popular in Department

This 4 page Class Notes was uploaded by Alison Holden on Tuesday September 13, 2016. The Class Notes belongs to M 145 at University of Hartford taught by Dr. Hadad in Fall 2016. Since its upload, it has received 28 views.

×

## Reviews for Calculus II: Week One notes

×

×

### What is Karma?

#### You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 09/13/16
Calculus II Week One Notes Calculus I Review Function: relationship between an independent and dependent variables. Every independent has 1 dependent Derivative: rate of change (slope) at any point of a line Y= f(x) Derivative can be represented by: dy/dx, y’, or f’(x) Constant of Integration 2 2 y = 6x + 3x + 1 vs y = 6x + 3x +2 The original functions are different due to the constant, however when taking the derivative, the answer is the same for both: y = 12x + 3. This creates a dilemma when going the opposite direction. When integrating a function, you must always account for the constant that may or may not be in the function by adding a + C. ∫ 12x+3 )ⅆx Ex: 6x +3x+C = ∫ f x dx Symbol for Integration: Properties of Integrals  If there is a constant multiplied by the function, you can move it outside the integral and multiply after o ∫Cf (x)ⅆx=¿ C ∫ f(x)ⅆx 2 2 o ∫6x ⅆx=6∫ x ⅆx  If there is more than one function inside an integral separated by addition or subtraction, you can separate them o ∫ f(x)+g x ⅆx=∫ f (x)ⅆx+∫g (x)ⅆx o ∫sin +cosx ⅆx = ∫sin x ⅆx+∫cos (x)ⅆx  The power rule of integration: xn+1 o ∫ x ⅆx= +C n+1 7+1 8 7 x x o ∫ x ⅆx= 7+1 +C= 8 +C Integration by substitution: ∫ x cos(x +2 )ⅆx Ex: x +2 Let u = Take the derivative: du = 4 x ⅆx 1 Rewrite integral in terms of u: 4 ∫cos u)ⅆu The u term covers the part inside the trigonometry and du covers both x and dx. However, you must add ¼ in front of integral to compensate for the 4 inside of du. 1 1 Integrate: ∫cosuⅆu= sinu+C 4 4 1 sin(x +2)+C Replace u: 4 Ex 2: ∫ √x+1ⅆx = ∫ (2x + 1)1/dx u= 2x + 1 du=2du 1 1 ∫( )ⅆx 2 3 1 2 2 1 3 ∕ 2 = 2 3 u = 3(2x+1 ) +c Definite Integrals b ∫ f (x)d(x=F b ⋅F (a) a Integral: Area under the curve to the x axis 3 ∫ (x −6x )ⅆx Ex: 0 4 x 2 Integrate: 4 −3x 34 2 0 4 2 Put in bounds: −3 3 )− [ ) −3 (0)] 4 4 81 Simplify: −27 = -6.75 4 Particle Motion S (t) t= time S= displacement s't) V (t) = V = instantaneous velocity Instantaneous velocity is the velocity a one single point on a graph. Average velocity is velocity from t = a to t = b A = dv/dt = s’’(t) A = Acceleration Displacement vs Distance Distance from origin. Total distance travel in time = t Ex: Find the displacement of the particle when 1≤t≤4 V(t=t −t−6 You must integrate in order to find the s(t) function:t −t−6 )ⅆx 3 2 t − −6x = 3 2 from 1 to 4 1 1 43 42 = 3− 26 1 ( ) – (3 − 2 −6 ( )−4.5 meters

×

×

### BOOM! Enjoy Your Free Notes!

×

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

## Why people love StudySoup

Bentley McCaw University of Florida

#### "I was shooting for a perfect 4.0 GPA this semester. Having StudySoup as a study aid was critical to helping me achieve my goal...and I nailed it!"

Amaris Trozzo George Washington University

#### "I made \$350 in just two days after posting my first study guide."

Jim McGreen Ohio University

Forbes

#### "Their 'Elite Notetakers' are making over \$1,200/month in sales by creating high quality content that helps their classmates in a time of need."

Become an Elite Notetaker and start selling your notes online!
×

### Refund Policy

#### STUDYSOUP CANCELLATION POLICY

All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email support@studysoup.com

#### STUDYSOUP REFUND POLICY

StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here: support@studysoup.com

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to support@studysoup.com