Calculate the definite integral ln xdx (E is above and 1 is below)
The original function of LNX is f (x) = xlnx-x
therefore
Definite integral ln xdx (e above 1 below)
=f(e)-f(1)
=0-(-1)
=1
If you don't know the original function, you can also use the partial integration method
RELATED INFORMATIONS
- 1. Questions about the concept of definite integral n ∑i²=(n(n+1)(2n+1))/6 i=1 Why? Why is that? Can you give the name and inference method of the relevant formula?
- 2. Definite integral problem: finding the definite integral of X / √ (1-x ^ 2) on [0,1]
- 3. How to calculate the definite integral of √ (1 + x ^ 2) from 0 to 1?
- 4. Why is the definite integral of the nth power of X on (0,1) 1 / N + 1?
- 5. How to find the definite integral of e to the power (- x) from negative infinity to 0 The specific problem is as follows: when x is greater than or equal to 0, find f (x) = (1 / 2) [∫ e ^ (- x) DX (integral lower limit is negative infinity, upper limit is 0)] + (1 / 2) [∫ e ^ (- x) DX (integral lower limit is 0, upper limit is x)]
- 6. Find the definite integral of the (- SX) power of e multiplied by the nth power of X from 0 to positive infinity. (n is a real number)
- 7. Find the area of figure enclosed by straight line x = 0, x = 1, y = 0 and curve y = x (x-1) Using the "four step curve" to solve the trapezoidal area of curved edge
- 8. The area of the figure enclosed by the curve y = ex, y = E-X, x = 1 is______ .
- 9. Let the plane figure d be bounded by the square of the curve y = x, the straight lines X = 1 and y = 0, and find the area s of D
- 10. The area of a figure enclosed by a curve y ^ 2 = x and a straight line x = 1?
- 11. The definition of definite integral 1. Y = x ^ 2 + 1 is integrable on [a, b]. Divide [a, b] n equally into ξ K (k is the subscript) (k = 1.2.3.4... N) the right end point of the cell is a + K (B-A) / N. how do you get the right end point? What does K (B-A) mean? 2. Why is LIM (n → + ∞) {B-A / n [n (a ^ 2 + 1) + B-A / N2a (1 + 2 +... N) + (B-A) ^ 2 / N ^ 2 (1 ^ 2 +... + n ^ 2)] equal to (B-A) [a ^ 2 + 1 + AB-A ^ 2 + (B-A) ^ 2 / 3]?
- 12. Using the definition of definite integral to prove... Ask for powerful help Using the definition of definite integral, it is proved that ∫ B (upper limit of integral) a (lower limit of integral) KF (x) DX = k ∫ B (upper limit of integral) a (lower limit of integral) f (x) DX (k is a constant)
- 13. The definition of definite integral Who can explain exactly what is definite integral Not too much
- 14. How to calculate definite integral by definition?
- 15. Definition of definite integral
- 16. What is the area of the trapezoid surrounded by the curve y = 1 / x, the straight line x = 1, x = 2 and the X axis?
- 17. Find the area of trapezoid surrounded by straight line x = 0, x = 2, y = 0 and curve y = x square!
- 18. Let the following functions be defined on the symmetric interval (- A, a) odd and even functions (1) The sum of two even functions is even and the sum of two odd functions is odd (2) Any function defined on a symmetric interval (- A, a) can be expressed as the sum of an odd function and an even function
- 19. The definite integral of an odd function on the symmetric interval about the origin must be 0. Why is it wrong?
- 20. The effect and significance of function parity and region symmetry on definite integral