What is the integration of Mod of X?

What is the integration of Mod of X?

The integral of |x| depends on the domain in which it is being integrated. For x>0, |x| = x. For x<0, |x| = -x. Thus, if |x| is integrated in the positive domain, the result obtained is x^2/2 + C.

What is the integral of 1 with respect to X?

Answer: The integral of 1/x is log x + C. Hence, the integral of 1/x is given by the loge|x| which is the natural logarithm of absolute x also represented as or ln x.

How do you remove modulus from integration?

The usual way to remove absolute value signs is to substitute in the definition: if you have |z| in your problem, then you split the problem into two subproblems: one where you add the condition z≥0 and one where you add the condition z≤0.

Can we integrate Modulus?

It is possible. By definition, Integration is nothing but the area under the curve. from figure just calculate the area for given limits and that would be the integration of mod x.

Why is the integral of 1 U ln U?

The reason the ∫x11udu=lnx is because that’s simply what it’s defined to be. Then the fundamental theorem of calculus tells us that the antiderivative must be the integrand and so ∫1xdx=lnx+C.

What is the integration of 1 U?

The integral of 1u with respect to u is ln(|u|) . Simplify. The answer is the antiderivative of the function f(u)=−1u f ( u ) = – 1 u .

How do you find the integral of Mod X?

The integral can be written as (x^2)*sgn (x)/2 +C. Note that this C is different from the earlier ones. The domain of this function is R- {0}. Integration of mod x is x 2 / 2 s g n x + c.

What is the integral of 1x?

Answers to the question of the integral of 1 x are all based on an implicit assumption that the upper and lower limits of the integral are both positive real numbers. If we allow more generality, we find an interesting paradox. For instance, suppose the limits on the integral are from − A to + A where A is a real, positive number.

What is the integral of modulus of X?

if X values are grater than or equal to zero(x>=0) then Integral of modulus of x is (x^2)/2 + c. if X values are less than zero i.e.,negative numbers(x<0) then Integral of modulus of x is -(x^2)/2 + c.

How does 1x → ∞ diverge to infinity?

As 1 x → ∞ as x → 0, we must use an improper integral. Thus, the integral diverges to infinity.