SOLUTION: The problem is stated as: {{{ (d/dx) int((sqrt(2+t^2)),dt,0,2)}}} I've done integral problems before but what is the purpose of the d/dx in front? that is throwing me off. I

Algebra ->  Finance -> SOLUTION: The problem is stated as: {{{ (d/dx) int((sqrt(2+t^2)),dt,0,2)}}} I've done integral problems before but what is the purpose of the d/dx in front? that is throwing me off. I      Log On


   

Question 1004964: The problem is stated as:
+%28d%2Fdx%29+int%28%28sqrt%282%2Bt%5E2%29%29%2Cdt%2C0%2C2%29
I've done integral problems before but what is the purpose of the d/dx in front? that is throwing me off. I don't know what this problem needs in order to be solved.
Please help
Thank you
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
If there are no x variables on either limit of integration, then the answer is simply 0. Here is why

The value of +int%28%28sqrt%282%2Bt%5E2%29%29%2Cdt%2C0%2C2%29 is simply a constant. We don't need to know what actual constant it is, but we definitely know it is NOT a variable. It's a fixed number. So +int%28%28sqrt%282%2Bt%5E2%29%29%2Cdt%2C0%2C2%29+=+C where C is a fixed number. The value of C is equal to the area under the curve from t = 0 to t = 2.

Taking the derivative of any constant leads to 0. +%28d%2Fdx%29+%28C%29+=+0. In a visual sense, all constant functions have graphs that are horizontal straight and flat lines. Any tangent line will have a slope of 0. So again, the derivative of a constant function is always 0.

In the end, +%28d%2Fdx%29+int%28%28sqrt%282%2Bt%5E2%29%29%2Cdt%2C0%2C2%29+=+0

Note: this only applies IF there are no x variables anywhere in the limits of integration.