0
For some functions the answer is relatively straightforward and you have a formula. For other functions, it may be possible, using numerical methods, to calculate the area under the function's curve. This will be a numerical answer to the problem under specific boundary conditions.
Add your answer:
Earn +20 pts
What is an antiderivative?
It is an inverse function of a derivative, also known as an integral.
What you say if a function whose derivative and antiderivative is same?
That means that either the function is equal to zero everywhere (y = 0), or it is the exponential function (y = ex).
How do you take the antiderivative of 1 over x?
The general formula for powers doesn't work in this case, because there will be a zero in the denominator. The antiderivative of 1/x is ln(x), that is, the natural logarithm of x.
Is there any other anti derivative of 1 divided by x?
The antiderivative of 1/x is ln(x) + C. That is, to the natural (base-e) logarithm, you can add any constant, and still have an antiderivative. For example, ln(x) + 5. These are the only antiderivatives; there are no different functions that have the same derivatives. This is valid, in general, for all antiderivatives: if you have one antiderivative of a function, all other antiderivatives are obtained by adding a constant.
What is the function of an antiderivative in calculus?
Anti-derivatives are a part of the integrals in the calculus field. According to the site Chegg, it is best described as the "inverse operation of differentiation."
What is the antiderivative of zero?
The antiderivative of a function which is equal to 0 everywhere is a function equal to 0 everywhere.
How integration is reverse process of differentiation?
For example, the derivate of x2 is 2x; then, an antiderivative of 2x is x2. That is to say, you need to find a function whose derivative is the given function. The antiderivative is also known as the indifinite integral. If you can find an antiderivative for a function, it is fairly easy to find the area under the curve of the original function - i.e., the definite integral.
What is an antiderivative?
It is an inverse function of a derivative, also known as an integral.
Let f be an odd function with antiderivative F. Prove that F is an even function. Note we do not assume that f is continuous or even integrable.?
An antiderivative, F, is normally defined as the indefinite integral of a function f. F is differentiable and its derivative is f.If you do not assume that f is continuous or even integrable, then your definition of antiderivative is required.
Can a function have more than one antiderivative?
yes, look at the function f(x)=3x^2 The antiderivative is x^3+C where C is the constant and is more than one value for C. In fact, 3x^2 will have an infinite number of antiderivatives.
Can anyone of can prove that antiderivative is wrong?
The way to disprove an antiderivative is to simply differentiate the function and see if it matches the integral expression. Remember that an antiderivative expression must include a term often coined "C-" an arbitrary constant. For example, ∫(x^3 +14x)dx= (1/4)X^4+ 7X^2 +C. To verify that this is correct, take the derivative. You get x^3 +14x.
What you say if a function whose derivative and antiderivative is same?
That means that either the function is equal to zero everywhere (y = 0), or it is the exponential function (y = ex).
What is the antiderivative of 2x?
The antiderivative of 2x is x2.
What is integral in math?
There are two main definitions. One defines the integral of a function as an "antiderivative", that is, the opposite of the derivative of a function. The other definition refers to an integral of a function as being the area under the curve for that function.
How do you take the antiderivative of 1 over x?
The general formula for powers doesn't work in this case, because there will be a zero in the denominator. The antiderivative of 1/x is ln(x), that is, the natural logarithm of x.
Is there any other anti derivative of 1 divided by x?
The antiderivative of 1/x is ln(x) + C. That is, to the natural (base-e) logarithm, you can add any constant, and still have an antiderivative. For example, ln(x) + 5. These are the only antiderivatives; there are no different functions that have the same derivatives. This is valid, in general, for all antiderivatives: if you have one antiderivative of a function, all other antiderivatives are obtained by adding a constant.
What is the anti-derivitive?
The inverse operation to the derivative. Also called the integral. If you're given the derivative of a function, you can find the function again by performing the antiderivative. Many answers will be possible, all differing by a single number, so you normally add a general constant to the end. Example : The derivative of 6x^2 is 12x. The antiderivative of 12x is 6x^2 + any number.
