定积分∫ (2到-2)[(4-x^2)^(1/2)*(sinx+1)]dx

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定积分∫(2到-2)[(4-x^2)^(1/2)*(sinx+1)]dx定积分∫(2到-2)[(4-x^2)^(1/2)*(sinx+1)]dx定积分∫(2到-2)[(4-x^2)^(1/2)*(si

定积分∫ (2到-2)[(4-x^2)^(1/2)*(sinx+1)]dx
定积分∫ (2到-2)[(4-x^2)^(1/2)*(sinx+1)]dx

定积分∫ (2到-2)[(4-x^2)^(1/2)*(sinx+1)]dx
原式=∫(2,-2) (4-x^2)^(1/2)*sinxdx + ∫(2,-2) (4-x^2)^(1/2)dx
因为f(x)=(4-x^2)^(1/2)*sinx是奇函数,所以∫(2,-2) (4-x^2)^(1/2)*sinxdx=0
所以原式=∫(2,-2) (4-x^2)^(1/2)dx
=2arcsin(x/2)+x/2*√(4-x^2)|(2,-2)
=-π-π
=-2π