Question Number 103669 by 175mohamed last updated on 16/Jul/20

prove that :  a) ∫_(−3) ^(−1) x^2 dx ≥∫_1 ^3 (2x−1)dx  b)∫_(−2) ^0 xdx ≤∫_0 ^2 (x^2  + x )dx  c)∫_1 ^4 (x^2  + 2)dx  ≥∫_2 ^5 (2x −5)dx  d)∫_(−π) ^(−((3π)/4)) cos 2x dx ≥∫_((3π)/4) ^π sin 2x dx

Answered by Aziztisffola last updated on 16/Jul/20

Just calculat each integral.

Answered by abdomathmax last updated on 17/Jul/20

a) ∫_(−3) ^(−1)  x^2 dx =_(x=−t)     ∫_3 ^1 t^2 (−dt) =∫_1 ^3 t^2  dt   wehave x^2 ≥2x−1 ⇒∫_1 ^3 x^2 dx ≥∫_1 ^3 (2x−1)dx  ....