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Find antiderivatives of the given functions.$$f(x)=\frac{3}{2}(6 x+1)^{1 / 2}(6)$$

Calculus 1 / AB

Chapter 25

Integration

Section 1

Antiderivatives

Integrals

Harvey Mudd College

Baylor University

University of Nottingham

Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

01:11

Find the antiderivatives $…

01:09

Find an antiderivative.

01:02

Find an antiderivative $F(…

01:37

01:25

Find the antiderivative.

01:16

Evaluate the integrals usi…

00:55

Find the most general anti…

01:17

01:30

Particular antiderivatives…

03:43

$$\text {Evaluate the foll…

All right. We want to find the anti derivative of the function after fact is equal to three half times X. Six X plus one to that. One half times six. This question is testing your knowledge of anti differentiation as a precursor of integration as such. We need to understand this concept entirely. So remember the anti derivative is just the inverse derivative function that bees if we understand how to take a derivative, These three rules the right, we can take the inverse of these rules to find an anti derivative for this problem. We need to use the both the power rule one and three. As I've highlighted the chain rule, the reason we need to use the chain rule is if we were to take the derivative of six X plus one of the one half, it would produce by a chain rule a factor of six Because of the parentheses derivatives six X. With one. Therefore we anti derive 6 61 and one half it has to absorb a factor of six to take the inverse, so we then have capital Fx. The anti derivative is three half 10 to 36 603 half the power rule 10 6/6, absorbing that factor of six by the chain rule. This gifts F x equals six x minus one of the three halfs.

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