the area under the curve is self explanatory and can be found by Integration or anti-deriviation. It can be used to find the area between a graph curve and the ‘x’ axis, between two given ‘x’ values.
This area is called the ‘area under the curve’ regardless of whether it is above or below the ‘x’ axis.
When the curve is above the ‘x’ axis, the area is the same as the definite integral but when the graph line is below the ‘x’ axis, the definite integral is negative.
A particle moving on a straight line of acceleration a = 5 - 3t, and its velocity is 7 at time = 2. If s(t) is the distance from the origin, find s(2) - s(1).
if a= 5 - 3t, the integral of a is v, so integral of a is, 5t - 3/2t^2 + c. so v= 5t- 3/2t^2 + c. if v=7 and t=2, c= v + 3/2t^2-5t...c= 7+ 3/2(2)^2 - 5(2)=3. so c=3...the the integral of v is s...which is the integral of 5t-3/2t^2 + 3...= 5/2t^2 - 1/2t^3 + 3t +c...s(2)-s(1)= 12-5=7...SOY EL EFE
FROM EARTH TO MARZ!!! that question is very simple!!!! just keep in mind that v = ds/dt and a = dv/dt. we have "a" if we integrate "a" we wud get v. remember we wud have a constant "c" we have to find this 'c' so we substitute v=7 and t = 2 into the equation of v. here now we can find 's" which is the integral of "v" When we get 's' just substitute s=2 and minus it from s=1
MISS!!! I HAVE A PROBLEM!!! IM SURE U HAVE NOTICED THAT MY COMMENTS ON THIS BLOG HAVE DRIED UP A BIT. ITS NOT THAT I SEE THIS BLOG AS A WASTE OF TIME OR ANYTHING. ITS JUST THAT I HAVE SOOOO MUCH PROJECTS AND ASSIGNMENTS TO DO WITH DEADLINES TO MEET. I MUST ADMIT IM LEARNING QUITE ALOT FROM THIS BLOG. I DONT HAVE ACCESS TO INTERNET AT HOME AND I TRY MY BEST TO AT LEAST POST A COMMENT ONCE IM IN SCHOOL. PLEASE UNDERSTAND!!!!
TO DANTEINTEGRATION IS JUST THE OPPOSITE OF DIFFERENTIATION. WHAT WUD U DIFFERENTIATE TO GET COS X??? SIN X OF COURSE!!!! SO THE INTEGRAL OF COS X IS SIN X. SIMILARLY WAT WILL U DIFFERENTIATE TO GET -SIN X??? NOT COS X???? SO THE INTEGRAL OF -SIN X IS COS X.
To Cokebaby!! You said "INTEGRAL OF COS X IS SIN X. SIMILARLY WAT WILL U DIFFERENTIATE TO GET -SIN X??? NOT COS X???? SO THE INTEGRAL OF -SIN X IS COS X."
Please explain this in a littler terms! others might be puzzled with what you are saying! you make it sound complicated!
tell me u have to integrate then u have to make c the subject of the formula and then substitute v=7 and t=2.WELL THAT WAS UNDERSTANDABLE TO ME THANKS PEOPLE
what i understand recently with integration is that yes it is opposite of diffrenciation.except that you dont multiply by the polynomial you add one to the power and then divide it by the power and thats merely what ur doing for integration
To find tghe area under a curve you must first find the integral of the equation the subsitute the to value found on the integral sign and then minus it from the the subsitution of the number at the bottom.
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28 comments:
the area under the curve is self explanatory and can be found by Integration or anti-deriviation. It can be used to find the area between a graph curve and the ‘x’ axis, between two given ‘x’ values.
This area is called the ‘area under the curve’ regardless of whether it is above or below the ‘x’ axis.
When the curve is above the ‘x’ axis, the area is the same as the definite integral
but when the graph line is below the ‘x’ axis, the definite integral is negative.
to add a little on the topic the area under the is boundby the limits that are given
the area under a curve connot be found, unless it is a closed by a reagion. meaning that u have to have two points on the x of y axis.
i tink area under the curve can be calculated by using the trapezoidal rule...
Hi
This section is for questions to solve on the topic in question. Real life or mathematical questions
Integrate 5cos x + 4x^5 + 8
5cos x + 4x^5 + 8
in tegrated form is 5 sin x+ 4/6 x^6 + 8x + c
A particle moving on a straight line of acceleration a = 5 - 3t, and its velocity is 7 at time = 2. If s(t) is the distance from the origin, find s(2) - s(1).
SPARKLE CAN I ASK WHY U INTEGRATED THE 8 isnt that a constant.
THIS IS HOW I WUD HAVE INTEGRATED IT.
add 1 to the power
4x^6 + 5 sin x + c
because c is the constant
correct me if im wrong
hey miss i kinda dont understan that question.
honestly
miss i still confuse but isnt the area under the curve the limits
if a= 5 - 3t, the integral of a is v, so integral of a is, 5t - 3/2t^2 + c. so v= 5t- 3/2t^2 + c. if v=7 and t=2, c= v + 3/2t^2-5t...c= 7+ 3/2(2)^2 - 5(2)=3. so c=3...the the integral of v is s...which is the integral of 5t-3/2t^2 + 3...= 5/2t^2 - 1/2t^3 + 3t +c...s(2)-s(1)= 12-5=7...SOY EL EFE
FROM EARTH TO MARZ!!!
that question is very simple!!!! just keep in mind that v = ds/dt and a = dv/dt. we have "a" if we integrate "a" we wud get v. remember we wud have a constant "c" we have to find this 'c' so we substitute v=7 and t = 2 into the equation of v. here now we can find 's" which is the integral of "v" When we get 's' just substitute s=2 and minus it from s=1
MARZ IF U DONT UNDERSTAND MY LAST COMMENT LUK PAPA VIGIL HELP U TOO!!!!!
marz, 8 aint no constant dred. what sparkle did was correct. you kinda confused dred. for the constant c you applying to, is something different.
EVERYONE!!!!!.....................
what is the difference when you integrate cosx and -sinx?
MISS!!! I HAVE A PROBLEM!!! IM SURE U HAVE NOTICED THAT MY COMMENTS ON THIS BLOG HAVE DRIED UP A BIT. ITS NOT THAT I SEE THIS BLOG AS A WASTE OF TIME OR ANYTHING. ITS JUST THAT I HAVE SOOOO MUCH PROJECTS AND ASSIGNMENTS TO DO WITH DEADLINES TO MEET. I MUST ADMIT IM LEARNING QUITE ALOT FROM THIS BLOG. I DONT HAVE ACCESS TO INTERNET AT HOME AND I TRY MY BEST TO AT LEAST POST A COMMENT ONCE IM IN SCHOOL. PLEASE UNDERSTAND!!!!
eh coke baby i agree!!!
MISS PLEASE EXCUSE MY NEGLECTION
OF THE BLOG I HAVE THE SAME STORY AS COKE BABY!!
projects weighing down heavy on men plus qiuz and moc exam wheyyyyyy
TO DANTEINTEGRATION IS JUST THE OPPOSITE OF DIFFERENTIATION. WHAT WUD U DIFFERENTIATE TO GET COS X??? SIN X OF COURSE!!!! SO THE INTEGRAL OF COS X IS SIN X. SIMILARLY WAT WILL U DIFFERENTIATE TO GET -SIN X??? NOT COS X???? SO THE INTEGRAL OF -SIN X IS COS X.
To Cokebaby!!
You said "INTEGRAL OF COS X IS SIN X. SIMILARLY WAT WILL U DIFFERENTIATE TO GET -SIN X??? NOT COS X???? SO THE INTEGRAL OF -SIN X IS COS X."
Please explain this in a littler terms! others might be puzzled with what you are saying! you make it sound complicated!
so Papa Vigil
tell me u have to integrate then u have to make c the subject of the formula and then substitute v=7 and t=2.WELL THAT WAS UNDERSTANDABLE TO ME THANKS PEOPLE
yeah miss, projects real plenty and time real limited. ah still tryin to post up blogs though.
TO NOTICE!!!!
It cant get more simplier than that. i cant xplain it much simplier than that. integration is just the opposite of differentiation!!!!
what i understand recently with integration is that yes it is opposite of diffrenciation.except that you dont multiply by the polynomial you add one to the power and then divide it by the power and thats merely what ur doing for integration
the area under the curve is understood to me that its the value between 2 x values.and that u must never get a negative value.
To find tghe area under a curve you must first find the integral of the equation the subsitute the to value found on the integral sign and then minus it from the the subsitution of the number at the bottom.
Rodrigrez makes an excellent point on how to find the area under a curve.
the area under a curve connot be found, unless it is a closed by a reagion. meaning that u have to have two points on the x of y axis
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