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9. If a curve is given by , where 0≤ t ≤4π and b is a constant, the length of the curve is ________

其他申論題

5. The integral In x dx =_______

6. The integralx =______

8. The temperature on the surface of a metal plate is T(x, y) =. The direction of the greatest increase in heat from point (3, 4) is_______； The rate of increase in the direction from point (3, 4) to point (6, 8) is _______.

1. Find the average of the function f(x) = x sin x between x =0 and x=π.

2. The eror functon erf(x) is defined as erf(x)=. Use this formula to find the integral .

3.For dx dy ,(1)sketch the region of integration； (2) switch the order of integration and evaluate the integral.

4. Evaluate the line integral ，where C. line segment from (1, 1) to (Hint:)

5.Find the area of the region Iying between the inner and outer loops of the limacon r(θ) =1-2sinθ.

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