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Symbolab is the best integral calculator solving indefinite integrals, definite integrals, improper integrals, double integrals, triple integrals, multiple integrals, antiderivatives, and more. An antiderivative of function f (x) is a function whose derivative is equal to f (x).
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Every continuous function f has an antiderivative, and one antiderivative F is given by the definite integral of f with variable upper boundary: = , for any a in the domain of f. Varying the lower boundary produces other antiderivatives, but not necessarily all possible antiderivatives.
If f (x) f (x) is the antiderivative of v (x), v (x), then f (x) + 1 f (x) + 1 is the antiderivative of v (x) + 1. v (x) + 1.
Learning Objectives. Find the general antiderivative of a given function. Explain the terms and notation used for an indefinite integral. State the power rule for integrals. Use antidifferentiation to solve simple initial-value problems.
2020年11月10日 · 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 \(f\); we use the notation \(\int f(x)dx\) to denote the indefinite integral of \(f\)
Calculus: How to find Antiderivatives, the formula for the antiderivatives of powers of x and the formulas for the derivatives and antiderivatives of trigonometric functions, antiderivatives and integral formulas, with video lessons, examples and step-by-step solutions.
IfF is an antiderivative of f, then the function G (x) = F (x) + C (C a constant) is also an antiderivative. Conversely, suppose F ,G are both antiderivatives to a function f on an interval ( a;b).
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