Question

What is the definite integral of zero?
(a) constant
(b) 1
(c) infinity
(d) None of these

Answer 1

Hint: To find a definite integral of such a simple quantity, we are to check what the needed derivation of the needed term. To check, we have, whenever we are trying to derive a constant term, we will get the value of the derivation is zero. So, in an opposite manner, we get that the constant term integrating zero.

Complete step by step solution:
According to the problem, we are trying to find the definite integral of the given value zero.
To start with, we have, the integral of 0 is C, because the derivative of C is zero. C represents some constant.
Also, it makes sense logically. Think about it like this: the derivative of the function is the function's slope, because any function f(x) = C will have a slope of zero at point on the function.
Consider a function, f(x) = K where K is any constant on the set of real numbers. When you differentiate f(x) with respect to x we get 0.
Going in reverse integrating indefinitely 0 would give K+C where C is the constant of integration. Since both K and C are constants we may replace it by another constant P.
In conclusion indefinite integration of 0 gives a constant that belongs to the set of real numbers.

So, the correct answer is “Option a”.

Note: Well, an integral looks at your velocity over time to determine the distance you've traveled away from some object since you started traveling. We can program your cruise-control to record velocities from other trips and use the recordings to control the velocity of your car, so that we still meet the same velocities over the entire trip. This will give an accurate measure of distance traveled from moment travel had begun, but you could be any starting distance away from our reference point. When the integral is zero, we know that the distance doesn't change, so that we only ever are some constant 'c' away from the reference point.