Integration

Question 1

What is the reverse chain rule?

Answer 1

Divide by the derivative of the inside function

Question 2

How do you find the area between 2 curves?

Answer 2

Find where the curves intersect by using simultaneous equations

See from sketch where the area is you’re looking for

Find the integral of(g(x)-f(x)) beteeen the x values of the points of intersection

Question 3

What does integration as the limit of a sum involve?

Answer 3

Splitting into really thin rectangles where the area of each is f(x) X delta x

Question 4

How do you integrate by substitution?

Answer 4

Choose a function which you can differentiate at call it u

Rearange to find dx and x in terms of you

Substitute all terms with x with terms involving u

The substitute every u with what it was before

Question 5

How do you integrate by parts?

Answer 5

Integral of u dv/dx dx = uv- intregral of v du/dx dx

Used to integrate a function multiplied by another function.

Call one u and one Dv/dx

Find u, dv/dx, du/dx and v

Substitute into the formula