$\ int \ int_D x ^ 2y \, dA$, where $D$ is the leading fifty percent of the disk with facility the beginning and also radius $5$.
when i connected whatever in, I obtained the dual important $$\ int_0 ^ \ pi \ int_0 ^ 5 r ^ 4 \ cos ^ 2 \ theta \ wrong \ theta \, dr \, d \ theta.$$ then I utilized $u$ alternative and also obtained $5 \ int u ^ 2 \, du =\ left. \ frac 5u ^ 3 3 \ appropriate \ vert _ \ theta=0 ^ \ theta=\ pi =-5/ 3 - 5/3 = -10/ 3$ yet that"s absolutely incorrect. I considered numerous instances, what am I doing incorrect below? I"m rather certain i have the right technique however something"s failing.
You have actually failed to remember to incorporate relative to $r$ as well as I have no suggestion where does your leading $5$ originates from.
$$\ int_0 ^ 5r ^ 4 \, dr =\ frac =5 ^ 4$$
\ start straighten \ int_0 ^ \ pi \ cos ^ 2 \ theta \ wrong \ theta \, d \ theta &= \ left. -\ frac \ cos ^ 3 \ theta 3 \ appropriate \ vert_0 ^ \ pi \ end straighten
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Review the provided important by transforming to polar collaborates. (just how to incorporate $\ wrong(r ^ 2)r$ relative to $r$?
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