find-antiderivatives-of-the-given-functions-fx10-x1-10-40-x-19-20-3

Question

Find antiderivatives of the given functions.
$$f(x)=10 x^{1 / 10}-40 x^{-19 / 20}$$

Tyler Moulton · Accepted Answer

All right. We want to find the anti derivative of the function F x is equal to 10 X to the 1/10 minus 40 X to the negative 19/20. This question is testing your knowledge of anti differentiation, other precursor to integration as such. And you have to have a solid understanding of this concept to proceed So remember that the anti derivative is just the inverse derivative. So if we understand derivative rule taken, we understand how to think and I directed by looking at the inverse, I have listed three comprehensive rules on the right for this problem. We only need to rule one to solve which is the power rule since for derivatives, it states TVs actually A is a actually a minus one. It holds by the inverse that the antidepressant XD A must be won over eight plus one times X to the A plus one. So we have for fx Capital FX is 10 times that over 11 x. 11 or 10 -40 times 20 actually won over 20. Mhm. Simplifying our constance gives final solution and the directive is 100 over 11 X 11 or 10 minus 800 x. To the 1/20.

Amit Srivastava · Answer

we have been given a function. Dfx equals 11 X rays to the part of tech. Let capital Geo fix be the anti derivative off small JFX. Now we know that the derivative off the function X rays to the part off 11 plus CVS sees a constant will be ableto 11 x rays to the part off then so therefore, the capital G affects the function will be equal toe X rays to the part of 11 plus C, which means the anti dedicate, if both dfx will be, will do the family off X rays to the part off 11 plus e there sees a constant.

Bruno Toledo · Answer

So this problem wants us to evaluate the indefinite integral of 11 X to the 10th power with respect to X. So the constant 11 comes out or another concept, as you call it a factory. This this constant factor, uh, which is 11 comes out of the indefinite in a group. So you still have extra the 10th inside and sultry to integrate extra the 10th or to find the anti derivative of extra. The 10th we use what&#x27;s called a power will rule for indefinite integral. So we&#x27;re gonna have remember, the 11 comes, Just bring it over. Right? So and then, with this exponents of 10 we&#x27;re going to add one to it. And at the same time, we&#x27;re going to divide this expression by the same exponents, right? And then this is an indefinite integral. So don&#x27;t forget, you gotta add the plus seat and the end. So that&#x27;s gonna be 11 x to the 11th divided by 11 plus c and then the 11th cancel out. So you just have X to the 11th Power plus C, and this right here gives you the family of anti derivatives of this function 11 x to the 10th power. So this is the answer right here.

Linh Vu · Answer

in this question were given the function F x equal agenda X squared plus one. And we need to find the anti derivative Captain F X. Yeah, We use a formal on fund of power room here. You get a good expert and this one off endless one plus a constant C. Yeah. For the first time here, we get equal to the expo entry on with three for the one here. We don&#x27;t need your hand up. Thanks. Here and now. We don&#x27;t forget your brother Constant. See your finest police say we know that I have observed in court you five and it we would&#x27;ve zone here in ISO hand and yeah, nafta would only to see their far doesn&#x27;t implies that we have that. And tiny river. There you go to the experiment tree on with drapers. This five

Amit Srivastava · Answer

a function given to us. This FX equals five X to the part of four. We need to find its anteed elevated. So we let the anti creativity function B f or fix. That means now we know that Let if effects be equal to express to the part of five plus e. Then the derivative off ffx will become equal to five x to the power off full. So therefore, the anti dead innovative function off ffx is equal toe FX, which is equal to actually part of five plus C where C is a constant.

Amit Srivastava · Answer

we are given a function that is F X is equal to X rays to the part of five minus two X rays to the part of minus to plus one. We need to find an antidote elevated for the function with satisfies the initial value off effort. One is equal to zero now the and did elevated function. F X will be equal to integral off the given function effects, which will be equal to integral off the function. Extra the part of five minus two extra the part of minus to plus one DX, which will become equal toe X rays to the part off. Six. Divided by six minus two X rays to the part off minus to plus fund divided by minus to plus one plus X plus C, which will be will do expecially part off six Divided by six plus cool divided by X plus X plus e. Now this is the value off the anti very, very function. Now we&#x27;re given the initial value that F at one is equal to zero. So putting that bigot, the value of see as f off one is equal to zero, which implies that one race to the part of six divided by six plus tolerated by one plus one plus C is equal to zero, which means one divided by six plus two plus one plus C is equal to zero that is civil common per week will do minus 19 divided by six now Putting the value off see in the anti derivative function will get the anted elevated function as a widow. X rays to the part of six Divided by six plus two, divided by X plus X minus 19 Divided by six

Problem

Find antiderivatives of the given functions. $$f(…

Problem 26 Easy Difficulty

Find antiderivatives of the given functions.
$$f(x)=10 x^{1 / 10}-40 x^{-19 / 20}$$

Answer

$F(x)=\frac{20}{11} x^{11 / 10}-80 x^{1 / 10}$

Related Courses

Basic Technical Mathematics with Calculus

Related Topics

Discussion

Top Calculus 1 / AB Educators

Grace H.

Catherine R.

Anna Marie V.

Kristen K.

Calculus 1 / AB Courses

Precalculus Review - Intro

Functions on the Real Line - Overview

Recommended Videos

Watch More Solved Questions in Chapter 25

Video Transcript

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

Grace H.

Catherine R.

Anna Marie V.

Kristen K.

Precalculus Review - Intro

Functions on the Real Line - Overview

What do you need help with?

Textbooks

Ask a question

Courses

AI Tutor

$F(x)=\frac{20}{11} x^{11 / 10}-80 x^{1 / 10}$

Basic Technical Mathematics with Calculus

Grace H.

Catherine R.

Anna Marie V.

Kristen K.

Precalculus Review - Intro

Functions on the Real Line - Overview

Allyn J. Washington, Richard S. EvansBasic Technical Mathematics with Calculus

Grace H.

Catherine R.

Anna Marie V.

Kristen K.

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus