How to check if the integral of a function is correct with a scientific calculator? As a calculus student I would like to know if there is any way to verify the "correctness" of an integral of a function using a calculator. 
I mean if have something like $f(x) = \cos(2x)$, then  $\int f(x) ~dx=\frac{1}{2}\sin(2x) + C$. 
Now, is there anyway to check if my answer is right using a scientific calculator? 
 A: Since you are solving for the indefinite integral of a function, you are solving for the anti-derivative. You can plug in the answer you got in any modern scientific calculator using the d/dx function and compare the results.
For example, let's say you are solving for the integral of cos(2x). You think the answer is sin(2x)/2 + C but you are not sure. All what you have to do is first, calculate the original cos(2x) using an arbitrary substitution for x (say 7) so you put cos(2*7) which is going to be ~0.136737
Now you can use the d/dx function of your calculator using the same value for x (notice that the c constant is not important):
d/dx(sin(2x)/2),x=7

your calculator is going to output ~0.136737. Since it is the same result, you did it successfully.
Quick tips:


*

*Whenever you are doing trigonometric calculus. Make absolutely sure that you are using the radian system in your calculator.

*If the result of the d/dx function in your calculator is so small, it is going to round it to 0. Watch out for that, you might want to use other numbers for x.
It's actually a life-saver. It's so helpful. My calculator is Casio fx-991ES PLUS for reference.
A: Here is a rather simple (but many times effective) method I share with my students. Say you have a function and you need to find the anti derivative. You think you found one. Let's make the integral a definite one. Choose a nice lower and upper value and plug them into your anti derivative and get an answer. Now take a graphing calculator like a TI 83/84 (just a scientific won't work) and plug in that function. Let the TI get the area under the curve with the CALC tool and compare that answer with yours. If they match, then you can bet that you got it right. For me as a student (and I am a still a student, will always be...) this has helped me a many times, in particular with eve numbered questions in books that have no answers. Sometimes an online integration tool comes up with weird (but correct) anti derivatives that differ substantially from mine (like with trig integrals) and so my method has proven to be effective...
