Question

evaluate ∫0-2a [x^a/2÷✓(2a-x)]dx​

Answer 1

Answer:

$I=∫ 2ax−x 2 ​ dx​ I=∫ a 2 −(x−a) 2 ​ dx​ Let t=x−adt=dx Therefore,I=∫ a 2 −t 2 ​ dt​ We know that∫ a 2 −x 2 ​ dx​ =sin −1 ( ax​ )+C Therefore,I=sin −1 ( at​ )+CI=sin −1 ( ax−a​ )+C Hence, this is answer.$

Step-by-step explanation: