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Answer :
The given integral ∫₀₇₃₂₅ sin(2 × (364.37 × 1485 / l²)) dl is divergent.
To evaluate the integral ∫₀₇₃₂₅ sin(2 × (364.37 × 1485 / l²)) dl, we can use a change of variables. Let's introduce a new variable
u = 364.37 × 1485 / l².
First, we need to find the limits of integration in terms of the new variable u. When l = 0, u = ∞, and when l = 7325, u = 0.
Therefore, the integral becomes:
∫∞₀ sin(2u) du
The integral of sin(2u) is -1/2 cos(2u). Applying this result to our integral, we have:
∫∞₀ sin(2u) du = [-1/2 cos(2u)] evaluated from 0 to ∞
Now, let's compute the values at the limits:
[-1/2 cos(2u)] evaluated from 0 to ∞ = [-1/2 cos(2∞)] - [-1/2 cos(2(0))]
= [-1/2 cos(∞)] - [-1/2 cos(0)]
Since cos(∞) is undefined, we can't determine the exact value of the integral. However, we can say that the integral diverges since the limits do not yield a finite value.
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