Question

Integral help?? Pretty please? :)

Answer 1

For -1 ≤ x ≤ 1, F(x) = the integral from -1 to x for sqrt(1 - t^2) dt

Answer 2

What does F(1) represent geometrically?
Evaluate F(1) and find F'(x).
Thanks for any help!

Answer 3

I can find F'(x) and evaluate F(1) but I don't know what F(1) represents geometrically.

Answer 4

i think substitution method will help
put t= cos(theta) first

Answer 5

To find F'(x) ?

Answer 6

I haven't learned about trig substitution yet...

Answer 7

How can I get the answer without that?

Answer 8

i dont know

Answer 9

Okay. Can you help with the first question? What does f(1) mean geometrically?

Answer 10

in order to determine f(1) geometrically
we need to know what is f(x) first

Answer 11

i feel something wrong
as x is going from -1 to 1
and t is going from -1 to x (which is not possible as per the problem)

Answer 12

Okay thanks for trying. :)

Answer 13

f(1) represents a point on the function at x=1
f' represents the slope of the tangent line to the function at a given x value

Answer 14

integral ... F(x), the integral of f(t) represents the area under the curve f(t) from 0 to x

Answer 15

F(1) defines a limit along the interval an endpoint to contain the area within.