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Find antiderivatives of the given functions.$$f(t)=6 t^{3}+12$$

$F(t)=\frac{3}{2} t^{4}+12 t$

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…

00:42

Find the indefinite integr…

01:11

Find the antiderivatives $…

01:04

Find an antiderivative.

01:17

Evaluate the integrals.

00:25

04:12

00:36

Evaluate the indefinite in…

01:37

00:53

Evaluate the integral by m…

00:57

we want to find the anti derivative of a function F of X is equal to six X cubed plus 12. To do so we need to have a solid understanding of anti differentiation which is a precursor integration and single variable count. So remember that the anti derivative is just the inverse derivative. That means we understand derivative rules. We can find an anti derivative for both six X cubed and 12. We only need to make use of rule one out of rules one through three are listed here. That is the power rule. Since the power rule states were derivatives. DDX actually A is a T A X to the a minus one. It holds that for the anti directive. Actually A we search for one over A plus one, actually a plus one. So taking anti derivative of fx we have capital F X equals six times 1/4 X to the fourth plus 12 X. On the second term for 12 we add a factor of expresses the constant. That's we have final solution. Capital F X is three halfs X to the fourth plus 12 X.

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