Bài 1 trang 112 SGK Giải tích 12. Tính các tích phân sau

Trung bình: 4,55
Đánh giá: 47
Bạn đánh giá: Chưa

a) -12121-x23dx ; b) 0π2sinπ4-xdx ;
c) 1221xx+1dx ; d) 02xx+12dx ;
e) 1221-3xx+12dx ; f) -π2π2sin3xcos5xdx.

 


a) -12121-x23dx=--12121-x23d1-x=-1-x23+123+1-1212=-31-x535-1212=-351253-3253=3104393-1.

b) 0π2sinπ4-xdx=-0π2sinπ4-xdπ4-x=--cosπ4-x0π2=cos-π4-cosπ4=0.

c) 1221xx+1dx=1221x-1x+1dx=lnx-lnx+1122=lnxx+1122=ln23-ln13=ln2.

d) 02xx+12dx=02xx2+2x+1dx=02x3+2x2+xdx=x44+2x33+x2202=343.

e) 1221-3xx+12dx=1224-3x-3x+12dx=1224x+12-3x+1dx=1224x+12dx-1223x+1dx=-4x+1122-3lnx+1122=43-3ln2.

g) -π2π2sin3xcos5xdx=-π2π212sin8x+sin-2xdx=12-π2π2sin8xdx--π2π212sin2xdx=-116cos8x+14cos2x-π2π2=0.