Question

定积分定义问题？

如图所示，我可以这样做吗，步骤有什么错误的地方请指出来感谢

Answer 1

lim(n->无穷) 1/n =0
lim(n->无穷) (1/n)cos(nx/n) =0
f(t)= cos(tx)
f(i/n)=cos(ix/n)
lim(n->无穷) (1/n){ 1+cos(x/n)+...+cos[(n-1)x/n] }
=lim(n->无穷) (1/n){ cos(x/n)+...+cos[(n-1)x/n] + cos(nx/n) }
=lim(n->无穷) (1/n) ∑(i:1->n) cos(ix/n)
=∫(0->1) cos(xt) dt
=(1/x)∫(0->1) cos(xt) dxt
=(1/x)[sin(xt)]|(0->1)
=(1/x) sinx