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
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
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.
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)
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
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.