Thank God this is for more points - CSlatt

• I can find the constant of an antiderivative given a coordinate pair that is included in that function.
• EX: Find the antiderivative of f(x) = 6x^2-4x+5when F(1) = 2. Then find F(2).
• So, to start find the antiderivative, which was the other learning target but I'll explain. For 6x^2, add one to the exponent and keep a 2 in front. For 4x, you add one to the exponent and keep a 2 in front. Make 5 5x. Then plug in 1 for x of the antiderivative because of the F(1) and set that equal to 2. Solve and get -3. Do the same as you did for F(1) but for F(2) and solve without setting equal to anything, and get 18.
  
  
  What trips me up is solving for the constant on an F(x)=?
• I can approximate the area under a curve via left and right endpoints for a given amount of rectangles.
• EX: Approximate the area under the curve using 6 rectangles for the function f(X) = 4 - 2x^2   on  [0, 12] Use both right and left endpoints.
• So, start by setting up a summation, using the number of rectangles for n. Use the equation for f(i/n) and plug in for f. Break the summation apart with subtraction and continue to break it down, pulling out 12/n and further solving for i^2. Eventually pull out what you can and cancel the n's out.
  
  
  What throws me off is not having an n at the top of the summation and having to solve for that
• I can use U-Substitution to integrate functions.
• EX: Integrate the function f(x) = x/sqroot(2x-5) on [3, 7].
• Assuming Christian forgot a dx on the end of the problem, make u everything under the square rooot, 2x-5. Du in turn, equals the derivative of that, 2, in terms of dx. Next plug in 7 and 3 into u to make them in terms of u, to now get 9 and 1. To balance out du=2dx, place a 1/2 in front of the integral, and set x= to 5/2. Now take the anitderivative of what you have and get 5/2u over u^3/2 over 3/2. Next plug x back in for u and do fundamental part 2 for 9 and 1.
  
  
  I am thrown off when having to choose the u and then plugging it back in