Raymond B. answered • 10/05/20
Math, microeconomics or criminal justice
sometimes it's easiest to reduce any trig function to sines or cosines, especially if you don't know what else to do.
secx=1/cosx, so
integral of -4sec^2(x) = -4/cos^2(x)
integral of cosx = sinx
derivative of sinx = cosx
derivative of cosx = -sinx
integral of -4/cos^2(x) = -4 times integral of cos^-2(x) = -4 times cos^-1x/-1 (-sinx) = 4sinx/cosx = 4tanx
Of course, this would have been much easier if you knew derivative of tanx = sec^2(x) and integral of sec^2(x)= tanx
evaluate at 0 to pi/3 or 60 degrees, tangent of 60 degrees is sqr3 = about 1.732, tangent of zero = zero
4tanx evaluated from 0 to pi/3 = 4sqr3 = 4 times about 1.732 = 6.928
