Solve Integral: y'=x^2, Point (2,6) on Graph

  • Thread starter Nanu Nana
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    Integrals
In summary, the conversation discusses finding the function for which y' = x^2 and (2,6) is a point on the graph. The attempted solution involves finding the integral of x^2, setting it equal to y(x), and solving for C. The correct answer is x^3-3y+10=0, which is equivalent to y = (x^3+10)/3.
  • #1
Nanu Nana
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Homework Statement



Determine the function for which y '= x ^ 2, and (2,6) is a point of the graph.

Homework Equations


y(x)=∫ x^2 dx

The Attempt at a Solution


I tried doing this but didn't get the right answer
y(x)=∫ x^2 dx
= x^3/3 +c

x=2 y=6

6=(2)^3 /3 +c
C= 3,33...
But according to the correctionpaper, its wrong . Answer should be x^3-3y+10 =0

How ??
 
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  • #2
Nope you just didn't notice that C=3,333...=10/3.
 
  • #3
But then shouldn't it be x3 +10/3 ??
 
  • #4
##x^3/3 + 10/3=y##
 
  • #5
How do we get that -3y ?
 
  • #6
So you mean you did the integral and finding C by yourself but you can't see the algebraic equivalence of ##(x^3+10)/3=y## and ##x^3+10-3y=0##??
 
  • #7
Yeah I couldn't see it but now I do . Thanks
 
  • #8
Ok you welcome, maybe you are not used in the perplexed form involving x and y, you are used in the form y=f(x).
 

1. What is an integral?

An integral is a mathematical concept that represents the area under a curve on a graph. It is used to find the total value or quantity of a function over a given interval.

2. How do you solve an integral?

To solve an integral, you need to use a specific method called integration. This involves finding the antiderivative of the given function, which is the function that when differentiated, gives the original function. Once the antiderivative is found, you can evaluate it at the given limits to find the definite integral.

3. What does y' = x^2 mean?

This notation represents the derivative of the function y with respect to x. In other words, it shows the rate of change of the function y with respect to the variable x. In this case, the derivative of y is equal to x^2.

4. How do you use a point on a graph to solve an integral?

A point on a graph can be used to find the value of the integral by plugging in the x-coordinate of the point into the antiderivative of the function. In this case, the point (2,6) means that when x = 2, y = 6. Therefore, the integral can be solved by plugging in x = 2 into the antiderivative of y = x^2.

5. Can you solve an integral without knowing the function?

It is not possible to solve an integral without knowing the function. The antiderivative of a function is unique and can only be found if the function is known. However, there are numerical methods that can be used to approximate the value of an integral without knowing the exact function.

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