Question

Find the area above x-axis for given function on given interval by using the Fundamental theorem of Calculus.
F(x)= 1+2sinx on [0,pi/2]

Answer 1

@DanJS

Answer 2

which ftc should I use first or the second?

Answer 3

is this just to integrate with respect to x over that interval?

Answer 4

F(upper)-F(lower)

Answer 5

I don't think so. I believe it has already integrated considering it uses an upper case F(x).. \[F(x)=\int\limits f(x)dx\]Probably just plug in the limits

Answer 6

from 0 to half pi, sin(x) is always a positive number, the function is always positive

Answer 7

do the integral of the function from 0 to half pi

Answer 8

find the area above x-axis- (for given function on given interval)

Answer 9

F(x) is the given function, the area under that is the definite integral value for the interval

Answer 10

I wasn't sure if the notation was specific. I was taught that it was, but I guess it may not be.

Answer 11

yeah that is what integrating will do, it can give you an exact area value for spaces that are curved in any way on the boundries

Answer 12

it has closed brackets towards it so I guess just teach me the way u is right I will check about that with my prof tmr

Answer 13

you see the pictures of 5 boxes, 10 boxes, infinite boxes, to estimate the area under curves

Answer 14

Yeah, I'm aware. But I was afraid that the question already presumes that it was integrated and just wants the student to plug in the limits, hence the "using fundamental theorem of calculus" part.

Answer 15

If notation is specific, then
\[\large \int\limits f(x)dx=F(B)-F(A)\]
I feel like we already have the left hand, now we just need to plug in the limits. But I could be wrong.

Answer 16

you see the pictures of 5 boxes, 10 boxes, infinite boxes, to estimate the area under curves- yes, I know that

Answer 17

but what are u trying to say I am confused now

Answer 18

the given function is F(x) = 1 + 2sin(x), they want the area between x-axis and that function.

That is what the fundamental theorem will do, you need to integrate, Just make the next F even larger. haha

Answer 19

X)

Answer 20

okay by using the first fundmental theorem?

Answer 21

\[\int\limits_{0}^{\pi/2}F(x)dx \]

Answer 22

that's the second i think

Answer 23

oh, you talking about that derivative of an integral , other thing?

Answer 24

no the ftc- I think the π/2F(x)dx u gave above is the second fundamental theo of calc

Answer 25

The second fundamental theorem of calculus is:
\[F(x)=\int\limits_{0}^{x}f(t)dt \implies \frac{ d }{ dx }[F(x)]=f(x)\]

Answer 26

@DanJS okay what is next plz explain me in terms of math I get confused when u talk in sentences.

Answer 27

X)

Answer 28

Integrate the function and you get

x - 2*cos(x)

then you take the upper bound and the lower bound and evaluate those in that x-2cos(x)

take the value of the upper - value of the lower, that is the answer