Expert: Scotto - 6/25/2009

Question
QUESTION: I want to integrate the following function:∫(2x3 – 3x2 + 5x – 2)dx and ∫(5sin2θ + 2cos4θ)dθ. Through self study I have worked out that they are 0.5x^4 + x^3 + 2.5x^2 – 2x + C and -5/2cos2θ + 0.5sin4θ+C. I would appreciate it if you could confirm my answers and/or correct them, please. Thank you, kind regards, Mike

ANSWER: The polynomial was done OK.
The trig problem was done OK.

Both look OK.

To see if the answers are correct, take the derivative.

The derivative of x^4/2 + x^3 + 5x^2/2 - 2xc + C
is 2x^3 + 3x^2 + 5x - 2, which is what was given to be integrated.

The derivative of -2.5cos2Θ + 0.5sin4Θ + c
is -2.5(-sin2Θ)2 + 0.5(cos4Θ)4 = 5sin2Θ + 2cosΘ,
which is what we given to be integrated.


---------- FOLLOW-UP ----------

QUESTION: Can I enter equations in a spreadsheet (excel etc) to find a derivative or integral, please? For instance I have the equation for the instantaneous voltage during the charge of a capacitor, viz v=V(1-e^t/T)where I know the values of t and T and V. Kind regards and thanks for last encouragement. Mike

Answer
You can't find the derivative of integral, but only a numerical approximation.  For derivatives, use a very small difference in x values to find the y value.  For integrals, use very small x values between the low point and high point and find the area of the rectangles between each of the points.  The height would be the value of the function and the width would be the difference in the x's for each interval.  The sum of the areas of all the rectangles would be the derivative.

The derivative of e^t is e^t.  
Here, the derivative of V((1-e^t)/T) is (V/T)(-e^T).



For new questions it is better to send it as a new question rather than a follow up.