Solve for x: S(0 to x) (t^3-2t+3)dt=4
I got a different answer from the back of the book. The back of the book said that x=1.63052 or x=3.09131. How am I suppose to solve this using a calculator?
I integrated, substituted the x, and simplified to get the following equation
x^4 - 4x^2 + 12x - 4 = 0
I then used Newton's Method and after 5 iterations I get x= 1.63052
So it appears the book is right.
I am not familar with that method. What is it that I do?
http://library.thinkquest.org/C006002/Pages/Newtons_Method_for_Solving_Equations.htm
explains the method
To solve this equation using a calculator, you can follow the steps below:
1. Start by entering the function f(t) = t^3 - 2t + 3 into the calculator.
2. Next, use the calculator's integral function to find the definite integral of f(t) from 0 to x. Note that different calculators might have different buttons or functions for integration, so refer to your specific calculator's manual for the exact steps to follow.
3. Set the value of the definite integral equal to 4 and solve for x. This means you will enter the equation as follows: ∫[0,x] (t^3 - 2t + 3)dt = 4.
4. Use the calculator's solve or root-finding function to find the values of x that satisfy the equation. Depending on the calculator, this might be labeled as "solve," "zero," or something similar. Enter the equation and let the calculator find the solutions.
5. Once you find the solutions, compare them to the values provided in the back of the book (x ≈ 1.63052 and x ≈ 3.09131) to verify your answer.
Keep in mind that calculator accuracy may vary, so it is always a good idea to double-check with different methods or tools to ensure the correctness of your answer.