A calculus problem by Hemanth Koundinya
Calculus
Level
1
Which of the following is an antiderivative of ?
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1 solution
y = Cos x
y + d y = Cos (x + d x)
d y = Cos (x + d x) - Cos x
d y = - 2 Sin (x + d x/ 2) Sin (d x/ 2)
d y/ d x = - Sin (x + d x/ 2) [Sin (d x/ 2)]/ (d x/ 2)
d y/ d x = - Sin x as d x --> 0
Integrate - Sin x d x = Cos x + k
Therefore, Integrate Sin x d x = - Cos x + constant.