Problem

Find the most general antiderivative of the funct…

01:15

Problem 20 Easy Difficulty

Find the most general antiderivative of the function.
(Check your answers by differentiation.)

$ f(x) = 1 + 2\sin x + 3/\sqrt{x} $

Name: find the most general antiderivative of the function check your answers by differentiation fx 1 2sin
Uploaded: 2021-06-03
Duration: 1 min 5 s
Channel: Numerade
Description: Find the most general antiderivative of the function. (Check your answers by differentiation.) $ f(x) = 1 + 2\sin x + 3/\sqrt{x} $

Answer

See explanation for result.

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Video Transcript

So for this problem we're looking to take the anti derivative of the given function. So our function is cases F of X equals one Plus 2 Cynics. Okay. Mhm. Plus three over the square root of X is our function. Um And I would like to write three over the square root of act as three times X to the negative one half. That's gonna help us in the long run when we keep the anti derivative. Well we know that the anti derivative of this constant, we're just the X. Class. We know that the anti drone of cynics is a negative co signs will have negative to cosign X class when we add we'll have three times when we add one to the exponents here. That'll be one half. So three X to the one half divided by one half will mean multiplied by to also be a six X. The one half final answer.

Carson M.

California Baptist University

Topics

Derivatives

Differentiation

Volume

Calculus: Early Transcendentals

Chapter 4

Applications of Differentiation

Section 9

Antiderivatives

Problem