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Integration errors

when you integrate 4x^5 + 3
you get 4x^6/6 + 3x + c

when you integrate 2
you get 2x + c

Exams is on calculus and matrix only

calculus
differentiation is gradient machine
give a point and you will get the gradient from gradient machine
differentiate polynomial, sin x, cos x, e^x , ln x
real life application RATE OF CHANGE is differentiation
VELOCITY = change in distance/ time
ACCELERATION = change in velocity /time

Integration
polynomial
sin x
cos x
area under curve
definite integral means point given so you can find the value of c

GOOD LUCK

Integration Questios

Integrate the following

1. dy/dx = 5x^3 + 2x^2 + 5

2. dy/dx = 6x + 1

3. dy/dx = 2

4. dy/dx = 8x^5 - 5x^3 + 4x

5. dy/dx = 7x^2 + 3x + 4

Integration +c being forgotten

Too many forgetting the + c in integration

question2
dy/dx=2x(x-3)
dy/dx=2x^2-6x
y=2/3x^3-3x^2

What about the + c
y=2/3x^3-3x^2 + c

To find the value of c use the point provided (3,6) x = 3 and y = 6
so c can be found

What about a question with v= and distance is required integrate yes but do not forget the +c

b)TO find the total distance travelled u need to integrate the (V) velocity.
v = 5t -3t^2 + 2
s= 5/2t^2 - t^3 + 2t

it must be
s= 5/2t^2 - t^3 + 2t + c

Errors

1. y = 6x^3 + 4x^2 -5x
when you differentiate how can the y remain y
dy/dx = 18x^2 + 8x -5

2. y^2 = x^3 + 16 is in the syllabus differentiating with 2 unknowns
some of you missed this class

differentiate term by term as normal and if the current term is a y term differentiate w.r.t y and then multiply by dy/dx

2y dy/dx = 3x^2

3. 1/y = 4x + 4
no downstairs
y^-1 = 4x + 4
differentiate term by term

-y^-2 dy/dx = 4

Common errors being made

1. y = 2x + 8/x^2 find dy/dx no downstairs y = 2x + 8x^-2 BUT when differentiating dy/dx = 2 -16x^-3 NOTE -2 -1 = -3
2. y = ln (2x + 3) use sub for m BUT dy/dm CANNOT be the same as dy/dm instead dy/dx must be= dy/dm * dm/dx

A particle moves in a straight line and at point P, it's velocity is given as v = 7t^2 - 5t +3. The particle comes to rest at point Q.

1. What is the acceleration at Q if it arrives at Q when t=7?
2. How far does the particle travel in t=1 to t=4?