Integration

Question 1

When you integrate without limits, what must you always add?

Answer 1

An arbitrary constant C!

This is because differentiation of any ion x2 +c gives the same product, so integration needs to keep the tin mind

Question 2

Formal nitration

Answer 2

Intregal sing

With the function
And respect to dx,

So f (expression) dx

Question 3

How to find arbitrary constant then (remember this all with no limitd)

Answer 3

Use extra data they find, derrive an equation fir c and go from there

Question 4

What does integrating within LIMITS ALLOW YOU TI DO

Answer 4

The integral at any point does not allwo you any info bevause of constant

However between two points the subtraction means that this cancels

And thus you get info

Question 5

So if I’m integrating between a to b what’s happening

Answer 5

Yiu integrate the function

Sub in b and take away from sub in a

Here the cos would cancel

Question 6

Nitration

Answer 6

Same as before, integral function respect to dx, with higher limit at top and lower at bottom

Then finding the new function swaure brackets and out limits on top again

Then it becomes g(b( - g(a)

Question 7

How to calculate area between two points on x axis and a curve

Answer 7

Often find the limits first

Then just outnit in

Question 8

What about below the axis? What should you do in these are aquesyiine

Answer 8

Just make sure quick sketch so yiu k is above and below

If below area csn’t be negative so make answer still positive

However in general fi they say find the value if this DEFINITE INTEGRAL INGNERWL YOU FONT!

Question 9

WHAT TO DO TO HELP with definite integrals vs for areas if one is below and one is above

Answer 9

The value of a definite integral if itsbelow the graoh and above can be done in ONE STEP BETWEEN ABSOLUTE LIMITE (as its just the vakue)

But if it’s area it MUST BE DINE IN OWRTS so the negative value is positive

Question 10

Bruh when they say bound to the x axis, make sure you IDENTIFY EACH SHADED REGION FIRST

Answer 10

and remember the area that’s under the graoh can be found by integration , when you use limits yiu use straight lines up anyways

Question 11

Remember difference if two squares is the same reverse too

Question 12

Remember negative indices , when integrating one less becomes more negative and integrating it becomes less negative

Question 13

Again make sure you can find it in sections first before rushing to start integrating, might have to use other rectangles etc too

Answer 13

Also what about symmetry?

TRU USE THAT, can make it easier !

Question 14

Even if you unsure about shape of the graoh still the maths will work and so even if negative when you thigh positive ither