计算定积分⑴∫(1,0)(x^2-1/x^2+1)dx ⑵∫(1,0)(x^4/1+x^2)dx
问题描述:
计算定积分⑴∫(1,0)(x^2-1/x^2+1)dx ⑵∫(1,0)(x^4/1+x^2)dx
答
1.原式=∫(上限1,下限0) dx - 2∫(上限1,下限0) dx/(x+1) =(x - 2arctanx)┃ (上限1,下限0) =(2 - π)/2 2.原式=∫(上限1,下限0) xdx - ∫(上限1,下限0) dx + ∫(上限1,下限0) dx/(x+1) =(x/3 - x + arctanx)┃ (上限1,下限0) =(3π - 8)/12