求下列定积分 1)∫[1,3]x^3dx 2)∫[1,4]√(x)dx 3)∫[π,2π]sinxdx 4)∫[0,1](1/4t^2-9)dt……
问题描述：
求下列定积分 1)∫[1,3]x^3dx 2)∫[1,4]√(x)dx 3)∫[π,2π]sinxdx 4)∫[0,1](1/4t^2-9)dt……
求下列定积分
1)∫[1,3]x^3dx
2)∫[1,4]√(x)dx
3)∫[π,2π]sinxdx
4)∫[0,1](1/4t^2-9)dt
5)∫[-1,0]e^(-x)dx
6)∫[-1,-2](x/x+3)dx
答
1)∫[1,3]x^3dx
=1/4*x^4=1/4*(3^4-1^4)=20
2)∫[1,4]√(x)dx
=2/3*x^(3/2)=2/3*4^(3/2)-2/3*1^(3/2)=14/3
3)∫[π,2π]sinxdx
=-cosx=-(cos2π-cosπ)=-2
4)∫[0,1](1/4t^2-9)dt
=1/12t^3-9t=1/12-9=-107/12
5)∫[-1,0]e^(-x)dx
=-e^(-x)=-(1-e)=e-1
6)∫[-1,-2](x/x+3)dx
=∫[-1,-2][1-3/(x+3)]dx
=x-3ln(x+3)
=-2-3ln1+1+3ln2
=3ln2-1