Question

用牛顿莱布尼茨公式计算下列定积分

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Answer 1

（6）原式=∫(0,π) |sinx-cosx|dx
=√2*∫(0,π) |sin(x-π/4)|dx
=-√2*∫(0,π/4) sin(x-π/4)dx+√2*∫(π/4,π) sin(x-π/4)dx
=√2*cos(x-π/4)|(0,π/4)-√2*cos(x-π/4)|(π/4,π)
=√2-1-(-1-√2)
=2√2
（8）原式=∫(-2,-1)x^4dx+∫(-1,1)dx+∫(1,3)x^4dx
=(1/5)*x^5|(-2,-1)+x|(-1,1)+(1/5)*x^5|(1,3)
=-1/5+32/5+1+1+243/5-1/5
=283/5
（10）原式=√2*∫(0,π/2) |sin(x-π/4)|dx
令t=x-π/4
原式=√2*∫(-π/4,π/4) |sint|dt
=2√2*∫(0,π/4) sintdt
=2√2*(-cost)|(0,π/4)
=2√2*(-√2/2+1)
=2√2-2

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请问这两道题怎么做？