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10 Νοε 2020 · We answer the first part of this question by defining antiderivatives. The antiderivative of a function \(f\) is a function with a derivative \(f\). Why are we interested in antiderivatives? The need for antiderivatives arises in many situations, and we look at various examples throughout the remainder of the text.
For the following exercises (1-5), show that [latex]F (x) [/latex] is an antiderivative of [latex]f (x) [/latex]. 1. [latex]F (x)=5x^3+2x^2+3x+1, \, f (x)=15x^2+4x+3 [/latex] Show Solution. 2. [latex]F (x)=x^2+4x+1, \, f (x)=2x+4 [/latex] 3. [latex]F (x)=x^2e^x, \, f (x)=e^x (x^2+2x) [/latex] Show Solution.
21 Δεκ 2020 · Answer \(f(x)=−\frac{1}{6}x^3−\dfrac{2}{x}+\dfrac{13}{6}\) In exercises 35 - 39, find two possible functions \(f\) given the second- or third-order derivatives
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.
The need for antiderivatives arises in many situations, and we look at various examples throughout the remainder of the text. Here we examine one specific example that involves rectilinear motion.
Antiderivative rules are some of the important rules to find the antiderivatives of different forms of combinations of a function. We can use these antiderivative rules to find the antiderivatives of product, quotient, sum, difference, scalar multiple, and composition of functions.
Example 1. Find Z x7 dx. Solution. An antiderivative of x7 is 1 8 x 8. Hence, Z x7 dx = 1 8 x 8 + C . Notice that we can check this result by di erentiating: F(x) = 1 8 x 8 + C F0(x) = x7 (The derivative of the constant C is just zero.) When calculating an inde nite integral, it is very easy to check your answer. You simply take
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σχετικά με: examples of antiderivatives math questions and solutions answerAutomatically Solve Problems. Algebra Geometry Trigonometry Calculus Number Theory Combinatorics Probability
