Question

定积分计算,怎么破,关键表达式变形?

Answer 1

令x=tgt,故dx=dt/[Cost]^2

原式=Integral{1/[(1/Cost)^2]^2 * dt/(Cost)^2,-π/4,π/4}

=Integral{(Cost)^2*dt ,-π/4,π/4}

=2*Integral{[1+Cos(2*t)]/2*dt ,0,π/4}

=π/4+1/2*{[Sin(2*t) ,0,π/4}

=π/4+1/2

=(π+2)/4