integral from 2 to 4 of 1/(|x-3|^{1/2)}

解答

\int_{2}^{4} \frac{1}{∣ x - 3 ∣ ^{\frac{1}{2}}} d x

4

求解步骤

\int_{2}^{4} \frac{1}{∣ x - 3 ∣ ^{\frac{1}{2}}} d x

拿掉绝对值

= \int_{2}^{3} \frac{1}{( - x + 3 ) ^{\frac{1}{2}}} d x + \int_{3}^{4} \frac{1}{( x - 3 ) ^{\frac{1}{2}}} d x

\int_{2}^{3} \frac{1}{( - x + 3 ) ^{\frac{1}{2}}} d x = 2

\int_{3}^{4} \frac{1}{( x - 3 ) ^{\frac{1}{2}}} d x = 2

= 2 + 2

化简

= 4

t an g e n t f (x) = x^{2} + x, at x = - 4, - 1

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