TÍNH TÍCH PHÂN SAU

Bài 8. Tính tích phân sau: (

^cos

)

0π π π

∫ ^e

^x

^{x xdx} ∫ ^e

^x

^xdx ∫ ^{x xdx I J}

+ = + = +

sin sin .sin

Giải: Ta có: (

^cos

)

^cos0 0 0π π

sin cos 1 .

( ) ( )

π

πcos cos cos cos cos0

I e xdx e d x e e e e

= ∫

^x

= − ∫

^x

= −

^x

0 = − − = −

e

0 0

=

π

∫ ^{Đặt  } _ ^{u x} _dv ⁼ _{= sin xdx} ^{⇒  } _ ^{du dx} _{v = −} ⁼ _{cos x}

J x xdx

.sin

π

π

π

π

( ) ( )

π π π

= ∫ = − + ∫ = − − + =

.sin cos cos cos 0.cos 0 sin

J x xdx x x xdx x

0 0

π

∫ + = + = − + π

sin 1

e

x

x xdx I J e

Vậy: (

^cos

)

π