Thread: Find lower bound of integral

Suppose 3x+7= integral from a to x (f(t)dt) What is the value of a?

I applied the fundamental theorem of calculus part 2 to get that f(x) = 3.

Then, I applied the first part of the fundamental theorem to get that the integral from a to x of 3 dt = 3x - 3a.

Looking at the solutions, it says that 3x - 3a = 3x + 7. Then you simply solve for a.

I don't understand why this relationship is true. How is 3x - 3a equal to 3x + 7?

You've done all the hard stuff.

3x+7 is given in the question as the value of the definite integral.

You have calculated the same integral as having a numeric value of 3x-3a.


So 3x+7 = 3x-3a. solve for a


If you're still confused you are probably over-thinking the problem. You have two expressions for the same definite integral, so they must be equal.

Thank you!