 # Can An Integral Have 2 Answers?

## How do you explain an integral?

In calculus, an integral is the space under a graph of an equation (sometimes said as “the area under a curve”).

An integral is the reverse of a derivative, and integral calculus is the opposite of differential calculus.

A derivative is the steepness (or “slope”), as the rate of change, of a curve..

## What is the integral of COSX?

Integrals of trig functions can be found exactly as the reverse of derivatives of trig functions. The integral of sinx is −cosx+C and the integral of cosx is sinx+C.

## What exactly is an integral?

The term “integral” can refer to a number of different concepts in mathematics. … In calculus, an integral is a mathematical object that can be interpreted as an area or a generalization of area. Integrals, together with derivatives, are the fundamental objects of calculus.

## What does a definite integral tell you?

The definite integral gives you a SIGNED area, meaning that areas above the x-axis are positive and areas below the x-axis are negative. That is why if you integrate y=sin(x) from 0 to 2Pi, the answer is 0.

## Why derivative of x2 is 2x?

So what does ddxx2 = 2x mean? It means that, for the function x2, the slope or “rate of change” at any point is 2x. So when x=2 the slope is 2x = 4, as shown here: Or when x=5 the slope is 2x = 10, and so on.

## What does a double integral give you?

Double integrals are a way to integrate over a two-dimensional area. Among other things, they lets us compute the volume under a surface.

## Why do we use triple integrals?

Triple integrals are the analog of double integrals for three dimensions. They are a tool for adding up infinitely many infinitesimal quantities associated with points in a three-dimensional region.

## How do you know when to use integration by parts?

Integration by parts is for functions that can be written as the product of another function and a third function’s derivative. A good rule of thumb to follow would be to try u-substitution first, and then if you cannot reformulate your function into the correct form, try integration by parts.

## What is the derivative of 2x?

To find the derivative of 2x, we can use a well-known formula to make it a very simple process. The formula for the derivative of cx, where c is a constant, is given in the following image. Since the derivative of cx is c, it follows that the derivative of 2x is 2.

## Why is integration so hard?

Integration is generally much harder than differentiation. This little demo allows you to enter a function and then ask for the derivative or integral. You can also generate random functions of varying complexity. … If integration seems hard – that’s because it really is!

## What is the integration of 1?

The definite integral of 1 is the area of a rectangle between x_lo and x_hi where x_hi > x_lo. In general, the indefinite integral of 1 is not defined, except to an uncertainty of an additive real constant, C. However, in the special case when x_lo = 0, the indefinite integral of 1 is equal to x_hi.

## What is integral 2x?

For example, what is the integral of 2x? You already know the derivative of x2 is 2x, so the integral of 2x is x2.

## Can a function have multiple integrals?

Multiple integrals have many properties common to those of integrals of functions of one variable (linearity, commutativity, monotonicity, and so on).

## Can you split a definite integral?

Internal addition In other words, you can split a definite integral up into two integrals with the same integrand but different limits, as long as the pattern shown in the rule holds.

## What is the integration rule?

This rule is essentially the inverse of the power rule used in differentiation, and gives us the indefinite integral of a variable raised to some power. Just to refresh your memory, the integration power rule formula is as follows: ∫ ax n dx = a. x n+1.

## What is the derivative of sin2x?

In a similar way, the derivative of sin(2x) with respect to 2x is cos(2x)….Using the chain rule to find the derivative of sin(2x)sin2x► Derivative of sin2x = 2cos(2x)sin (2x)► Derivative of sin (2x) = 2cos(2x)2 more rows•Oct 6, 2020

## What is the integral sign called?

Historical notation The notation for the indefinite integral was introduced by Gottfried Wilhelm Leibniz in 1675. He adapted the integral symbol, ∫, from the letter ſ (long s), standing for summa (written as ſumma; Latin for “sum” or “total”).