Today I reviewed Riemann sums. In order to help me review I watched a Khan Academy video.
https://www.khanacademy.org/math/integral-calculus/indefinite-definite-integrals/riemann-sums/v/simple-riemann-approximation-using-rectangles
It explains how the Riemann sums are used to approximate the area under a curve. Because it is an approximation it does not give us an exact value, but sort of an idea of one. You break the curve up into rectangles and solve for the area of each one and add them up.
Monday, April 6, 2015
Sunday, April 5, 2015
Review 4/5
Today I reviewed antiderivatives and indefinite integrals. To help me review I watched a Khan Academy video. https://www.khanacademy.org/math/integral-calculus/indefinite-definite-integrals/indefinite_integrals/v/antiderivatives-and-indefinite-integrals
In this video it explains the relationship between derivatives and antiderivatives. When taking the derivative of a function any constant value becomes a 0, and any x value is multiplied by its exponent and also subtracting one from the original exponent. Some examples are
x^2 + 1 ----> 2x
x^4 + x^3 + 3 ------> 4x^3 + 3x^2
When taking the antiderivative, also known as the indefinite integral, you take the coefficient of the x value and make it the exponent. For any constant you multiply it by x. Finally you must add a +C to the function. You must do this because there could be a value whether it is 0, 1, 10 ....
Some examples are
2x ---> x^2 +C
3x^2 +5x -4 -----> x^3 + (5x^2)/2 -4x +C
In this video it explains the relationship between derivatives and antiderivatives. When taking the derivative of a function any constant value becomes a 0, and any x value is multiplied by its exponent and also subtracting one from the original exponent. Some examples are
x^2 + 1 ----> 2x
x^4 + x^3 + 3 ------> 4x^3 + 3x^2
When taking the antiderivative, also known as the indefinite integral, you take the coefficient of the x value and make it the exponent. For any constant you multiply it by x. Finally you must add a +C to the function. You must do this because there could be a value whether it is 0, 1, 10 ....
Some examples are
2x ---> x^2 +C
3x^2 +5x -4 -----> x^3 + (5x^2)/2 -4x +C
Friday, April 3, 2015
Review 4/3
Today I decided to review parametric equations. To help me while I reviewed my notes I additionally watched a Khan Academy video helping explain what parametric equations actually are.
https://www.khanacademy.org/math/precalculus/parametric_equations/parametric/v/parametric-equations-1
In the video it explains that both x and y are functions of time. Through the use of parametric equations we can determine the direction and path of an object. Additionally you can also determine a third parameter, Z, on a three-dimensional plane. You can also determine the slope of a tangent line, velocity functions, acceleration functions, and speed.
I also google searched problems with their solutions to help me understand and practice. http://tutorial.math.lamar.edu/problems/calcii/parametriceqn.aspx
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