大专数学1、求积分∫=1/a^2-x^2*dx (常数a≠0)
2、求定积分∫上限是1下限是0 x^3dx
3、求定积分∫上限是л/2下限是0 x^2sin xdx
①∫1/(a^2-x^2)dx
=[1/(2a)]∫[1/(a-x)+1/(a+x)]dx
=[1/(2a)][-ln|a-x|+ln|a+x|]+C
=[1/(2a)]ln(|a+x|/|a-x)]+C
②∫ x^3dx
=(x^4)/4|=1/4
③∫ x^2sin xdx
=-∫ x^2d(cosx)
=-(x^2)cosx|+2∫ x(cosx)dx
=2∫ xd(sinx)
=2xsinx|-2∫ sinxdx
=л+2cosx|
=л-2
。
①∫1/(a^2-x^2)dx
=[1/(2a)]∫[1/(a-x)+1/(a+x)]dx
=[1/(2a)][-ln|a-x|+ln|a+x|]+C
=[1/(2a)]ln(|a+x|/|a-x)]+C
②∫ x^3dx
=(x^4)/4|=1/4
③∫ x^2sin xdx
=-∫ x^2d(cosx)
=-(x^2)cosx|+2∫ x(cosx)dx
=2∫ xd(sinx)
=2xsinx|-2∫ sinxdx
=л+2cosx|
=л-2
。
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