Question
Find the exact area under half of one arch of the sine curve, which is given by integral sin(x) dx from 0 to pi/2
Find the exact area under half of one arch of the sine curve, which is given by integral sin(x) dx from 0 to pi/2
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Koala Tutor
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To find the area under half of one arch of the sine curve, we need to evaluate the integral of sin(x) with respect to x from 0 to π/2.
∫ sin(x) dx = -cos(x) + C
To evaluate this integral, we substitute the upper limit (π/2) and lower limit (0) into the antiderivative:
[-cos(π/2) + C] - [-cos(0) + C] = [0 - (-1) + C] - [1 + C] = 0 - (-1) - 1 = 0 + 1 - 1 = 0.
Therefore, the exact area under half of one arch of the sine curve is 0.
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