Change to polar coordinate and evaluate $\int\limits_0^{2a}\int\limits_0^{\sqrt{2ax-x^2}}\dfrac{x}{\sqrt{x^2+y^2}}$dydx

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Change to polar coordinate and evaluate

$\int\limits_0^{2a}\int\limits_0^{\sqrt{2ax-x^2}}\dfrac{x}{\sqrt{x^2+y^2}}$ dydx

written 8.8 years ago by

teamques10 ★ 69k

modified 3.2 years ago by

pedsangini276 • 4.8k

Mumbai University > First Year Engineering > sem 2 > Applied Maths 2

Marks : 3

Year : 2014

engineering mathematics

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written 8.8 years ago by

teamques10 ★ 69k

• modified 8.8 years ago

The region of integration is bounded by $y = 0$ and $y = \sqrt{2ax-x^2}$

$Y^2=2ax-x^2 \\ X^2+y^2-2ax=0$

Adding $+a^2$ both side we get

enter image description here

$X^2-2ax+a^2+y^2=a^2 \\ (x-a)^2+y^2=a^2$

The equation is of circle with center at $(a, 0)$ and radius is a

The region of integration is also bounded by $x = …

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