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mediumNATPYQs Based Test - 10 : Application of TheoremsElectrical Engineering
2 marks

As shown in the figure, 𝐶 is the arc from the point (3, 0) to the point (0, 3) on the circle 𝑥² + 𝑦² = 9. The value of the integral is _____ (up to 2 decimal places).

image

Correct Answer

0-0

Solution & Step-by-step Explanation

_C^ ≤ft( y^2 + 2yx )dx + ≤ft( 2xy + x^2 )dy

According to Green’s theorem

_C^ Mdx + Ndy = _S^ ≤ft( {Nx - My} )dxdy

Here, M = y² + 2yx

N = 2xy + x²





_C^ ≤ft( y^2 + 2yx )dx≤ft( 2xy + y^2 )dy

= _C^ ≤ft( 2y + 2x - 2y - 2x )dxdy = 0

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Try it yourself before checking the explanation above.

As shown in the figure, 𝐶 is the arc from the point (3, 0) to the point (0, 3) on the circle 𝑥² + 𝑦² = 9. The value of the integral is _____ (up to 2 decimal places).

image

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