You should have a list of standard integrals, if you haven't got one then get one. Later, it helps if you can commit them to memory.
The one you need here is
This is my first time evaluating integrals on my own and, unfortunately, I just can't seem to get it. As easy as they may seem, integrals are giving me such a hard time, even the simplest ones are proving to be a challenge.
I need help evaluating the integral below:
I ended up with 15ln(-1)-15ln(-3)=DNE, but I'm almost certain I got it wrong.
One of the first things you should have learned about "definite integrals" (actually, the definition) is that if F is an anti-derivative of f (that is, if dF/dx= f) then .
Actually, yes, finding anti-derivatives is, typically harder than differentiating- although evaluating definite integrals should not be more difficult than evaluating any functions. There is a general distinction in mathematics between "direct problems", where we are given a specific definition or formula, and "inverse problems" where we are to "reverse" some direct problem. For example, if I told you that and ask you to find y when x= 3, that would be easy- just do the arithmetic in that formula. But if I told you that y= 3 and asked you to find x,, that would be a much more difficult problem- and there might be many solutions or none.
We learn, in introductory Calculus, a formula for the derivative of a function so finding a derivative can always go back to using that formula (though we can also use the many "theorems" for special cases derived from that formula). That's a direct problem. But an anti-derivative of f, say, is only defined as "a function whose derivative is f". We don't have a direct formula to use, we have to try to "remember" a function whose derivative is the given function. That's the "inverse" problem.