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kolezko [41]
3 years ago
15

How do i find the area between the two curves

Mathematics
1 answer:
viktelen [127]3 years ago
4 0
A=22/10

A=integral(a,b) [f(x)-g(x)]dx

Since the function is even (the function is mirrored over the y axis) we can evaluate the integral from 0 to 1 and then multiply our answer by 2 since we have the same area on each side of the y axis.

We get A=2*int.(0, 1)[(x^2)-(-2x^4)]dx

Now we can integrate by term.

2*[int.(0, 1)[x^2]dx+int(0, 1)[2x^4]dx]

Now factor out constants.

2*[int(0,1)[x^2]dx+2int(0,1)[x^4]dx]

Now integrate.

2*[(x^3/3)|(0,1) + 2*(x^5/5)|(0,1)]

Now solve.

2*[(1/3)+2*(1/5)]

=22/10

Hope you can decipher what I wrote!
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The inverse of the function x^7 is x^-7 and it is also a function.

An inverse function or an anti function is defined as a function, which can reverse into another function.

A standard method to find inverse of a function is to set y=f(x)

let y= f(x)=x^7

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thus f^{-1}(y)=\sqrt[7]{y}

thus f^{-1} (x)=\sqrt[7]{x}

(To verify this if a function is inverse or not we are required to check for the identity)

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Therefore, The inverse of the function x^7 is x^-7 and it is also a function.

For further reference:

brainly.com/question/2541698?referrer=searchResults

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