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

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