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Determine the value of a that makes $F(x)$ an antiderivative of $f(x)$$$f(x)=3 x^{2}, F(x)=a x^{3}$$

Calculus 1 / AB

Chapter 25

Integration

Section 1

Antiderivatives

Integrals

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Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

01:02

Find an antiderivative $F(…

00:44

Decide which function is a…

01:51

Show that $F(x)=\frac{1}{3…

01:22

Find an antiderivative.

01:17

00:53

02:23

Find the antiderivative $ …

01:34

Find the antiderivative $F…

01:43

Find the general antideriv…

02:19

Find an antiderivative for…

we want to find the constant A. Such that f of x equals a execute is an anti derivative of lower case F of x equals three X square. This question is challenging our knowledge of anti differentiation as a precursor to integration. So we need to understand this topic, remember that the anti derivative is an inverse derivative function. Thus we need to know DDX or rather derivative rules to understand anti directly rules. So I was the powerful product rule and chain rule on the right. In this particular problem we see that for three X squared converting to its anti derivative, we need to use the inverse power rule so it's rid of extra is 80 x minus one. The anti rid of of extra. I should be one over A actually a plus one. Thus we can perceive the entire delivery with this in mind. Thus we have F one equals three times one third X. Q. Or execute. Thus we solve for a such that are F one is equal to R. F, so for X equals F one we have a equals one

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