Evaluate the following integral ∫√(a^2-x^2 ) dx

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hamza

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2022-05-18

Evaluate the following integral ∫√(a^2-x^2 ) dx

Mathematics,

hamza

2022-05-18

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Put x=a sin⁡θ
∫√(a^2-a^2 〖sin〗^2 θ) a cos⁡θ dθ
=a^2 ∫〖〖cos〗^2 θ〗 dθ
=a^2 ∫〖(1+cos⁡2θ)/2 dθ〗=a^2/2 (θ+1/2 sin⁡2θ )+c
=a^2/2 (θ+sin⁡θ cos⁡θ )+c

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