The output ofIntegrate[Sin[x], {x, 0, 1}]is a.1 - Cos[1]b.1 - Sin[1]c.Sin[1]d.Cos[1]
Question
The output of Integrate[Sin[x], {x, 0, 1}] is
a. 1 - Cos[1]
b. 1 - Sin[1]
c. Sin[1]
d. Cos[1]
Solution
The integral of Sin[x] from 0 to 1 is equal to -Cos[x] evaluated from 0 to 1.
Step 1: Find the antiderivative of Sin[x], which is -Cos[x].
Step 2: Evaluate -Cos[x] at x = 1 and x = 0.
Step 3: Subtract the two results to get the definite integral.
So, -Cos[1] - (-Cos[0]) = -Cos[1] + Cos[0] = -Cos[1] + 1.
Therefore, the answer is a. 1 - Cos[1].
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