Download presentation

Presentation is loading. Please wait.

Published byAnabel Treadway Modified over 3 years ago

1
By: Zack Broadhead

2
When you take the derivative of a number with no variable it is just ‘0’. Y=5x+4, (dy/dx)=5+0 When you antidifferentiate an equation the result must have a “+ C” on the end because you don’t know what the constant number was.

3
Integrate equation. Tack “+C” onto the end. Plug in initial values. Solve for “C”. Plug “C” into integrated equation.

5
∫ (dy)=∫x dx Y=x 2 /2+C Y=3 and x=2 so: (3)=(2) 2 /2+C C=1 Y=x 2 +1

6
∫(dy)=∫Cos(x) dx Y=Sin(x)+C Y=1 and x=п/2 so: 1=Sin(п/2)+C C=0 Y=Sin(x)+0

7
∫(dy)=∫(x 2 +x) dx Y=(x 3 /3)+(x 2 /2)+C Y=1, and x=1 so: 1=1/3+1/2+C 1=5/6+C C=1/6 Y=(x 3 /3)+(x 2 /2)+1/6

8
∫(dy)=∫(1/x) dx Y=ln(x)+C Y=2 and x=1, so: 2=ln(1)+C C=2 Y=ln(x)+2

9
∫(dy)=∫(Sin(2x)) dx Y=-(Cos(2x))/2+C Y=1/2 and x=0, so: ½=-(Cos(2(0)))/2+C C=1 Y=-Cos(2x)/2+1

11
A. y=x 3 -2 May have accidentally subtracted “C”. B. y=6x-2 May have derived instead of integrated. C. y=x 3 +2 Correct answer! D. y=x 3 -998 Plugged wrong points in.

12
A. y=√((4/5)x 5 –(123/5)) Used wrong points. B. y=√((4/5)x 5 +(16/5)) Correct! C. y 2 /2=(2/5)x 5 +(8/5) Not simplified. D. y=8x 3 -6 Derived instead of integrated.

14
Answer: Y=x 2 -x+5 ∫(dy)=∫(2x-1) dx Y=x 2 -x+C Y=11 and x=3, so: 11=(3) 2 –(3)+C C=5 Y=x 2 –x+5

15
http://planetmath.org/encyclopedia/InitialValueProblem.html http://en.wikipedia.org/wiki/Initial_value_problem http://www.vias.org/calculus/14_differential_equations_01_split006.html

16
By: Zack Broadhead

Similar presentations

OK

4.1 Antiderivatives and Indefinite Integration Definition of Antiderivative: A function F is called an antiderivative of the function f if for every x.

4.1 Antiderivatives and Indefinite Integration Definition of Antiderivative: A function F is called an antiderivative of the function f if for every x.

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on spinal cord injury Ppt on condition monitoring Ppt on leverages business Ppt on trial and error definition One act play ppt on apple Ppt on eddy current probe Ppt on javascript events list Ppt on series and parallel circuits lab Ppt on condition monitoring vibration Ppt on water our lifeline assistance