What is the integral of the first derivative?

If the derivative of the original function is Riemann integrable, then the integral of the derivative is equal to the original function plus a constant. That’s the second part of the fundamental theorem of calculus .

What is integral of derivative?

the short answer is that the integral of the derivative is the original function, up to a constant.

Does the integral equal the derivative?

The conclusion of the fundamental theorem of calculus can be loosely expressed in words as: “the derivative of an integral of a function is that original function”, or “differentiation undoes the result of integration”. so we see that the derivative of the (indefinite) integral of this function f(x) is f(x).

What is the integral of 2?

Integration Rules

Common Functions	Function	Integral
Constant	∫a dx	ax + C
Variable	∫x dx	x2/2 + C
Square	∫x2 dx	x3/3 + C
Reciprocal	∫(1/x) dx	ln|x| + C

How to use the integral calculator to integrate a function?

Step 1: Enter the function you want to integrate into the editor. The Integral Calculator solves an indefinite integral of a function. You can also get a better visual and understanding of the function and area under the curve using our graphing tool. Integration by parts formula:? u d v = u v-? v d u. Step 2: Click the blue arrow to submit.

How do you find the derivative of an indefinite integral?

Since the derivative of a constant is 0, indefinite integrals are defined only up to an arbitrary constant. For example,∫ sin(x)dx= −cos(x)+constant ∫ s i n ( x) d x = − c o s ( x) + c o n s t a n t, since the derivative of −cos(x)+constant − c o s ( x) + c o n s t a n t is sin(x) s i n ( x).

How does xmaxima calculate integrals?

Maxima takes care of actually computing the integral of the mathematical function. Maxima’s output is transformed to LaTeX again and is then presented to the user. The antiderivative is computed using the Risch algorithm, which is hard to understand for humans. That’s why showing the steps of calculation is very challenging for integrals.

What is the definite integral of f(x)?

The definite integral of f (x) f (x) from x = a x = a to x = b x = b, denoted ∫b a f (x)dx ∫ a b f (x) d x, is defined to be the signed area between f (x) f (x) and the x x axis, from x= a x = a to x= b x = b. Both types of integrals are tied together by the fundamental theorem of calculus.