高数：积分∫[√2,0]1/(4+2x^2)dx
问题描述：
高数：积分∫[√2,0]1/(4+2x^2)dx
答
∫(0到√2) 1/(4+2x²) dx令x=√2*tany,dx=√2*sec²y dy4+2x²=4+2(√2*tany)²=4+2*2*tan²y=4+4tan²y=4(1+tan²y)=4sec²y当x=0,y=0;当x=√2,y=π/4原式=√2*1/4∫(0到π/4) se...