What does it mean when an integral is equal to 0?

So if the integral comes to be zero it means that the total algebraic sum of the area is zero . For the function sinx you can see the intefral is zero for limits 0 to pi . But if you plot the graph the geometric area is not zero under the curve but the area below the x axis is taken negative which yields the answer 0.

Can an integral be equal to zero?

Expressed more compactly, the definite integral is the sum of the areas above minus the sum of the areas below. (Conclusion: whereas area is always nonnegative, the definite integral may be positive, negative, or zero.)

What is an integral from 0 to 0?

It should also be noted that the definite integral of 0 over any interval is 0, as ∫0dx=c−c=0.

Which integral or integrals have a value of zero?

Therefore, the definite integral is always zero.

Why is the integral of an odd function zero?

The integrand is an odd function (i.e. f(-x) = –f(x)), and the integrand of an odd function over a symmetric interval is zero. This is because the region below the x-axis is symmetric to the region above the x-axis as the following graph shows. The derivative of an odd function is an even function and vice versa.

What is the double integral of 0?

That double integral is telling you to sum up all the function values of x2−y2 over the unit circle. To get 0 here means that either the function does not exist in that region OR it’s perfectly symmetrical over it.

What is an odd function times an odd function?

An even function times an odd function is odd, and the product of two odd functions is even while the sum or difference of two nonzero functions is odd if and only if each summand function is odd. The product and quotient of two odd functions is an even function.

What are the integration formulas?

List of Integral Formulas

• ∫ 1 dx = x + C.
• ∫ a dx = ax+ C.
• ∫ xn dx = ((xn+1)/(n+1))+C ; n≠1.
• ∫ sin x dx = – cos x + C.
• ∫ cos x dx = sin x + C.
• ∫ sec2x dx = tan x + C.
• ∫ csc2x dx = -cot x + C.
• ∫ sec x (tan x) dx = sec x + C.

What is the integral under any point always zero?

The integral under any point is always zero since there is no area to a point. Basic. The integral of a function in between two points. That’s why there a number on the top of the integral sign and a number at the notion of an integral sign.

What is the integral of 0 with the derivative of C?

The integral of 0 is C, because the derivative of C is zero. Also, it makes sense logically if you recall the fact that 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. Therefore ∫0 dx = C. (you can say C+C, which is still just C).

What is the integral of the function whose slope is zero?

The integral of 0 is C, because the derivative of C is zero. Also, it makes sense logically if you recall the fact that 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.

Why are the integrals of odd intervals always zero?

Those integrals are clearly zero because of the geometry of odd functions on those intervals. Question is incomplete it should be definite integral and it is not valid for indefinite integral.