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?
ln2
Integral 1 ~ 2 1 / x = 1 ~ 2 LNX = ln2-ln1 = LN2
RELATED INFORMATIONS
- 1. Definition of definite integral
- 2. How to calculate definite integral by definition?
- 3. The definition of definite integral Who can explain exactly what is definite integral Not too much
- 4. 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)
- 5. 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]?
- 6. Calculate the definite integral ln xdx (E is above and 1 is below)
- 7. 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?
- 8. Definite integral problem: finding the definite integral of X / √ (1-x ^ 2) on [0,1]
- 9. How to calculate the definite integral of √ (1 + x ^ 2) from 0 to 1?
- 10. Why is the definite integral of the nth power of X on (0,1) 1 / N + 1?
- 11. Find the area of trapezoid surrounded by straight line x = 0, x = 2, y = 0 and curve y = x square!
- 12. 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
- 13. The definite integral of an odd function on the symmetric interval about the origin must be 0. Why is it wrong?
- 14. The effect and significance of function parity and region symmetry on definite integral
- 15. If a function is odd in a symmetric interval, then its definite integral in this interval is zero?
- 16. Can y = 1 / X be defined as a definite integral? How to integrate [1,2] if it is over energy Can y = √ (1-x ^ 2) be used for definite integral [- 1,1] without geometric meaning? Is it possible to use definition method for integral?
- 17. Definite integral of 3 / 2 of function (square of 1-x) In the interval 0 to 1
- 18. It is known that there is no intersection point between the image of a first-order function and the line y = 2x + 1, and the area of the triangle bounded by its image and the x-axis and y-axis is 9. The analytic expression of the first-order function is obtained It's OK before 4 o'clock today,
- 19. Find the volume of the body of revolution of the ellipse x ^ 2 / 4 + y ^ 2 / 6 = 1
- 20. Find the volume of the body of revolution generated by a circle (X-5) ^ 2 + y ^ 2 = 16 rotating around the Y axis