4.1a
In this lesson we learned how to find the antiderivitave, which is basically the reverse of finding the derivative. All you have to do is add 1 to the exponent and then divide the term by that new exponent, and then add C.
4.1b
In order to integrate trig functions, all you have to do is know the derivatives of the trig functions and then work backwards from there.
Ex:
The derivative of tanx is sex(^2)x. So the integral of sec(^2)x is tanx.
To solve a differential equation that has a specific solution, you have to integrate the derivative, and that will give you your general solution +C.
In order to find the value of C, you need to plug in the point (initial condition into the general solution, solve for C) and rewrite the particular solution. When you are given the second derivative, you do the same process twice: once to get the derivative and once again to get the original function.
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REAL WORLD CONNECTION:
Chapter 4 Section 4.1b (Integrating Trig Functions)
Depending on what you choose to be your career, trig functions definitely come into play. For instance for electrical engineers, they use integrating trig functions to calculate the measurement of something called a “sinusoidal signal.” In order to find the measurement, they would need to integrate the signal. Also, they need to use integrating trig functions when trying to find low-pass and high-pass filters.
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