用牛顿-莱布尼茨公式计算定积分.

①原积分=∫(0到π)√[(sinx)^2-2sinxcosx+(cosx)^2]dx
=∫(0到π)√(sinx-cosx)^2dx
=∫(0到π/4)(cosx-sinx)dx+∫(π/4到π)(sinx-cosx)dx
=(sinx+cosx)(x=π/4)-(sinx+cosx)(x=0)+(﹣cosx－sinx)(x=π)－(﹣cosx－sinx)(x=π/4)
=2√2.
②原积分=∫(-2到-1)x^4dx+∫(-1到1)dx+∫(1到3)x^4dx
=(1/5×x^5)(x=-1)-(1/5×x^5)(x=-2)+x(x=1)-x(x=-1)+(1/5×x^5)(x=3)-(1/5×x^5)(x=1)
=283/5.