Thread: definite integrals question

p218 ex22a q25

i can only do it by using calculator. i want to know if i can do it manually

= (1/16)[sin(arctan(3/4) -sin(arctan(0)]

arctan(3/4).
opp side = 3
adj side = 4
So,
hypotenuse = 5
And so,
sin(arctan(3/4)) = opp/hyp = 3/5

arctan(0).
opp side = 0
adj side = 1
So,
hypotenuse = 1 -----actually, no hypotenuse.
And so,
sin(arctan(0)) = opp/"hyp" = 0/1 = 0 -----this is only for comparison.
Of course, if tan(tetha) = 0, then theta = 0
And sin(0) = 0 also.

Hence,
= (1/16)[3/5 -0]
= 3/80