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Finding the derivative of F (x) = sin ^ 3 · 1 / X
-3(sin(1/x))^2acos(1/x)/x^2
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- 1. Definite integral T ^ (n-1) * f (x ^ N-t ^ n) upper limit x lower limit 0
- 2. If f (x) has continuous derivatives in [1, + ∞), and satisfies X-1 + X ∫ (upper limit x, lower limit 1) f (T) DT = (x + 1) ∫ (upper limit x, lower limit 1) TF (T) DT, find f (x) The answer is f (x) = x ^ (- 3) * e ^ (1-1 / x),
- 3. In the derivation process of [∫ (0, x) TF (T) DT] 'explained by experts, the result should be XF (x), or XF (x) -∫ (0, x) f (T) DT
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- 10. Let f (x) be a differentiable function, definite integral (x, 0) (t-1) f (x-t) DT = 0, find f (x)
- 11. If f (x) is continuous and f (x) = x + (x ^ 2) ∫ (0,1) f (T) DT, find f (x)
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- 13. It is proved that the continuous function f (x) satisfies: ∫ (0 to 1) f (TX) DT = f (x) + xsinx
- 14. Let f (x) satisfy ∫ f (TX) DT (from 0 to 1) = f (x) + xsinx
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