Thread: Antiderivatives

Find the general antiderivative of the function below.
P(t) =

Find the general antiderivative of the function below.

F(t) =


Find the general antiderivative of f(x) = 6x.

F(x) =





Find the general antiderivative of the function below.
G(x) =




Find an antiderivative F(x) with F '(x) = f(x) and F(0) = 0. f(x) = sin(x)
F(x) =




Evaluate the indefinite integral below.




Evaluate the indefinite integral below.


i need some help with these bad johnnys...any help would be killer...thanks

mathlete

Originally Posted by mathlete

Find the general antiderivative of the function below.
P(t) =

Hint: what is the derivative of sec(x)? what about tan(x)?

Find the general antiderivative of the function below.

F(t) =

note that $\displaystyle \frac {t^4 + 1}t = t^3 + \frac 1t$

for the first part, use the fact that $\displaystyle F(t) = \int f(t)~dt$

now, $\displaystyle \int x^n~dx = \frac {x^{n + 1}}{n + 1} + C$ .....this is known as the power rule for integrals

for the second part, Hint: what is the derivative of ln(x)?

Find the general antiderivative of f(x) = 6x.

F(x) =

use the power rule

Find the general antiderivative of the function below.
G(x) =

use the power rule (Hint: you need to change the function a bit, to make it look like the form that the power rule applies to)

Find an antiderivative F(x) with F '(x) = f(x) and F(0) = 0. f(x) = sin(x)
F(x) =

Hint: what is the derivative of -cos(x)?

what is the anti-derivative of sin(x)? what if we plug in x = 0 into the anti-derivative?

Evaluate the indefinite integral below.

Hint: what is the derivative of arctan(x)?

Evaluate the indefinite integral below.

use the power rule