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

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

Calculus 1 / AB

Chapter 25

Integration

Section 1

Antiderivatives

Integrals

Missouri State University

Campbell University

University of Michigan - Ann Arbor

Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

00:49

Finding antiderivatives Fi…

01:32

Find all the antiderivativ…

00:53

Find an antiderivative $F(…

00:45

01:45

Particular antiderivatives…

00:47

01:04

Find an antiderivative.

01:17

01:11

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.

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