Definite integral of high school mathematics .3 ∫ - 1 how to find the original derivative of 2x ^ 5 in 2x ^ 5DX? What are the good steps What kind of thinking should be used to think about how to find this problem first and then how to deal with it

Definite integral of high school mathematics .3 ∫ - 1 how to find the original derivative of 2x ^ 5 in 2x ^ 5DX? What are the good steps What kind of thinking should be used to think about how to find this problem first and then how to deal with it

Because it is x ^ 5, the original function must be x ^ 6
Can be set to c * x ^ 6, derivative is 6C * x ^ 5 = 2 * x ^ 5
So C = 1 / 3

Find the area of the figure enclosed by parabola y = x ^ 2-1, straight line x = 2, y = 0
But the answer is 8 / 3
Is the answer wrong? ╮(╯▽╰)╭

If the intersection point of parabola y = x ^ 2-1 on the positive half axis of X axis is (1.0), then it is
The area enclosed by parabola y = x ^ 2-1, straight line x = 2, x = 1
1/3x³-x
1/3(2³)-2-[1/3(1³)-1]
=4/3

Circle and line
The hypotenuse of right triangle ABC has a fixed length of 2m. Take the midpoint o of hypotenuse BC as the center of the circle and make a circle with a fixed radius of N. the extension line of BC intersects two points P and Q. verify that | AP | ^ 2 + | AQ | ^ 2 + | PQ | ^ 2 is the fixed value

It is proved that: let a point coordinate in right triangle ABC be a (x, y), then B (- 1,0), C (1,0) according to known, we can get P (- N, 0), q (n, 0), then AB ^ 2 + AC ^ 2 = BC ^ 2 (x + 1) ^ 2 + y ^ 2 + (x-1) ^ 2 + y ^ 2 = 42x ^ 2 + 2Y ^ 2 + 2 = 4x ^ 2 + y ^ 2 = 1AP ^ 2 + AQ ^ 2 + PQ ^ 2 = (x + n) ^ 2 + y ^ 2 + (x-n) ^ 2 = 2x ^ 2 + 2Y ^ 2

Circle and line
1. In the plane rectangular coordinate system xoy, it is known that the center of circle X & # 178; + Y & # 178; - 12x + 32 = 0 is Q, and the line L passing through point P (0,2) with slope k intersects circle Q at two different points a and B. the value range of real number k is obtained
2. Given circle C: X & # 178; + Y & # 178; + ax + 2Y + A & # 178; = 0, fixed point a (1,2), if there are two tangents of circle C passing through point a, then the value range of real number a is——
3. The line L passes through the point (- 4,0) and intersects with the circle (x + 1) ² + (Y-2) ² = 25 at two points a and B. If AB = 8, then the equation of the line L is——
4. Solve the equation of the circle with chord length 6 which is cut on the x-axis through two points a (1,2), B (3,4)
Process or general idea

1. Let pf intersect X axis at C, then the triangle POC is equal to the triangle QBC, so the slope of Pb is - 1, because the tangent moves between PA and Pb, so K is greater than - 1 and less than 0.2

Space analytic geometry, solving linear equation
This line passes through M (- 1,0,4) and is parallel to the plane U: 3x-4y + Z-10 = 0
At the same time, it intersects with the line L: x + 1 = Y-3 = Z / 2
Find the line equation
I can see some content in the first and second conditions. How to use the third condition? It's better to do it concretely. If it's too troublesome, you can say the general method. Thank you
What's the use of this?
Plane vector? Plane normal vector? And then multiply it by the direction vector of the line = 0? I'll do it

The known point m and the known line L form a plane, and the line should be in this plane

Given that the abscissa of the intersection of line L and line y = 2x + 1 is 2, and the ordinate of the intersection of line y = - x + 2 is 1, the expression of line L is obtained

y=2x+1
X = 2, then y = 4 + 1 = 5
So the intersection is (2,5)
y=-x+2
y=1
So 1 = - x + 2
x=1
So the intersection (1,1)
Put two points in
5=2k+b
1=k+b
k=4,b=-3
So y = 4x-3

What is the symmetry equation of straight line in space analytic geometry?
Such as the title

The symmetric point of point P (U, V, w) with respect to line L: (x-a) / M = (y-b) / N = (z-c) / P is denoted as point Q (x, y, z). (1) determine the plane equation of plane m passing through point P with vector [M, N, P] as normal vector. M (x-u) + n (Y-V) + P (z-w) = 0. (2) determine the coordinates of the intersection r of plane m and line L