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153

Part of 2006 Today's Calculation Of Integral

Problems(1)

Today's calculation of Integral 153

Source: Waseda University entrance exam/Science and Engineering 1980

9/6/2006
Draw the perpendicular to the tangent line of the ellipse x2a2+y2b2=1 (a>0, b>0)\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\ (a>0,\ b>0) from the origin O(0, 0).O(0,\ 0). Let θ\theta be the angle between the perpendicular and the positive direction of xx axis. Denote the length of the perpendicular by r(θ).r(\theta). Calculate ∫02πr(θ)2 dθ.\int_{0}^{2\pi}r(\theta )^{2}\ d\theta.
calculusintegrationconicsellipsetrigonometryanalytic geometrygraphing lines