Antiderivative Problems Math

You can represent the entire family of antiderivatives of a function by adding a constant to a known antiderivative. We use the notation int f x dx to denote the indefinite integral of f initial value problem a problem that requires finding a function y that satisfies the differential equation dfrac dy dx f x together with the initial condition y x 0 y 0. So if f x is the antiderivative of f x then the family of the antiderivatives would be f x c.

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A function f x is an antiderivative of f on an interval i if f x f x for all x in i.

Antiderivative problems math. Set up the integral to solve. My question is i find the anti derivative for prime x 0 004x 100 then what do i do with the 5000. Math ap college calculus ab integration and accumulation of change the fundamental theorem of calculus and definite integrals. In ancient times mathematics was defined since the science of numbers and shapes.

The most general antiderivative of f x is the indefinite integral of f. I am sure it s simple. Free math problem solver answers your algebra geometry trigonometry calculus and statistics homework questions with step by step explanations just like a math tutor. The fundamental theorem of calculus and definite integrals.

This video shows how to solve a motion problem using antiderivative mathematical technique. Find the anti derivative 2x. Antiderivatives and indefinite integrals. I m stumped on these problems.

The function can be found by finding the indefinite integral of the derivative. It has been determined that the marginal cost of producing x processorcs is c prime x 0 004x 100. Find the anti derivative a f t 2e t 2 sint f 0 0 f pi 0 b f x 3 sqrt 1 x 2. If the fixed cost is 5000 find the cost of producing x processors.

It is no further possible to describe it in several sentences. We use the notation displaystyle int f x dx to denote the indefinite integral of f initial value problem. Math help forum home algebra pre calculus geometry trigonometry calculus advanced algebra discrete math differential geometry differential equations number theory statistics probability business math challenge problems math software. Mathematics like other branches of science has evolved over time.

What i have to say now is going. What is the antiderivative. Algebra pre calculus geometry trigonometry calculus advanced algebra discrete math differential geometry differential equations number theory statistics probability business math challenge problems math software. The fundamental theorem of calculus and definite integrals.

Mathematics is one of the oldest sciences in human history. The reverse of differentiating is antidifferentiating and the result is called an antiderivative. Antiderivative a function f such that f x f x for all x in the domain of f is an antiderivative of f indefinite integral the most general antiderivative of f x is the indefinite integral of f. The fundamental theorem of calculus and definite integrals.

Write as a function.