Integration Flashcards

1
Q

How to integrate?

A

Opposite of differentiate
- Increase square number by 1
- Divide by that square number

e.g. 3x^2 = 3x^3/3 = x^3

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2
Q

After every integration, what must u always add at the end?

A
  • + C, cuz apparently we don;t know if we gat that or not so ya
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3
Q

What’s integrals for?

A

Finding an area under a graph
- People who bored of the trapezium rule, so they were like “fuck it” and they made a super smart formula.

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4
Q

How to use integrals? (calculator edition)

A
  • u have the equation (3x^2 - x + 4)
  • Top of f is a point in graph
  • Bottom is same
  • Ye just place everything as is in calculator

Tho formula we have is this:

b^f^a f(x) dx

(b at top, a at bottom)

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5
Q

How to use integrals (not calculator edition)

A
  • So u have the equation (3x^2 - x + 4)
  • Integrate it (x^3 -x^2/2 + 4x)
  • Ok and now u need the points for the certain area under graph:
    a = 1, b = 2
  • Sub em in the integrated equation:
    For b = 2^3 - 2^2/2 + 4(2), For a = 1^3 - 1^2/2 + 4(1)
  • And well, ye u minus them:
    b - a = area under graph
    Who knows what they equal? = 9.5
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6
Q

Rq tips for integrals?

A
  • Well first off, u’ll probably have to find the coordinates urself first, they give u equation of the curve so, ya gl.
  • Might be simultaneous equations or just factorising type shi, woulda just said some e.g. but meh
  • Additionally, be smart about it, cuz they’ll also tell u to find the area of shaded region.
  • So in this case, u’ll probably have to either do 2 separate integrals, and minus them. OR, could just be a simple ass area of triangle, and minus n stuff.
  • Really tho main thing, get ur points, use ur brain on integrals, and bam u got it.
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