Let R Be the Region in the First Quadrant Bounded $x ^ { 2 } + y ^ { 2 } = 1$

question 13

Essay

Let R be the region in the first quadrant bounded between the circle $x ^ { 2 } + y ^ { 2 } = 1$ and the two axes.Then $\int _ { R } \left( x ^ { 2 } + y ^ { 2 } \right) d A = \frac { \pi } { 8 }$ Let $\bar { R }$ be the region in the first quadrant bounded between the ellipse $25 x ^ { 2 } + 9 y ^ { 2 } = 1$ and the two axes.
Use the change of variable x = s/5, y = t/3 to evaluate the integral $\int _ { x } \left( 75 x ^ { 2 } + 27 y ^ { 2 } \right) d A$

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