Find the area bounded by one arc of the cycloid x = a ( t − sin t ) , y = a ( 1 − cos t ) , and the x -axis.

Question

Find the area bounded by one arc of the cycloid x = a ( t − sin t ) , y = a ( 1 − cos t ) , and the x -axis. ​

TestHub · Accepted Answer

0 ≤ t ≤ 2 π , d t d x ​ = a ( 1 − cos t ) . A = a 2 ∫ 0 2 π ​ ( 1 − cos t ) 2 d t . ​ ( 1 − cos t ) 2 = 2 3 ​ − 2 cos t + 2 1 ​ cos 2 t . F ( t ) = 2 3 t ​ − 2 sin t + 4 sin 2 t ​ . A = a 2 [ F ( 2 π ) − F ( 0 )] = 3 π a 2 ​ . ​

Mathematics - Area Under Curves Question with Solution | TestHub

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