Assignment3

Remember to take the derivative of what you want to substitute in the integral. Because when we use the method of substitution, we actually change the variable, the whole process changes (the variable and the limits). We need to transfer it completely to get the correct value.
If you see a polynomial under a root sign that you cannot take its square root directly , think about substituting the variable with some form of trigonometric functions. There are some characteristics of trigonometric functions that are easy to be converted into a form that can be taken square root of, are favorable for elimination of the variables elsewhere and are easy to differentiate.
If it doesn’t work for one way of substitution, don’t quit, try another. For example, if t doesn’t work, try t square; if sin(x) doesn’t work, try cos(x),etc. It is hard for beginners to foresee if a method could work, because unexpected things happen all the time. Sometimes a variable can be eliminated; and sometimes we think it can be but it actually can’t.

mathematics