Question

问两道微积分题1. ∫sin(πx)cos(πx) dx2.∫0~3 ｜x^2-4｜dx (｜就是绝对值符号)请给详细过

Answer 1

1.

∫sin(πx)cos(πx) dx = ∫sin(2πx)/2 dx = -cos(2πx)/4π + C

2.

∫0~3 ｜x^2-4｜dx = ∫0~2 ｜x^2-4｜dx + ∫2~3 ｜x^2-4｜dx

= ∫0~2 (4 - x^2)dx + ∫2~3 (x^2 - 4)dx

= (4x - (1/3)x^3)|0~2 + ((1/3)x^3 - 4x)|2~3

= -3

没验算啊,数不一定准,但做法是这样