Finding the original function of definite integral (2-x ^ 2) ^ (3 / 2)

Finding the original function of definite integral (2-x ^ 2) ^ (3 / 2)

Let x = √ 2sint
∫(2-x)^(3/2)dx=4∫(cost)^4dt=∫1+cos2t+(cos2t)^2dt=∫3/2+2cos2t+1/2*cos4tdt=
3/2*t+sin2t+1/8*sin4t+C
Just replace the original function with X

∫ [(1 + 2x ^ 2) ^ 2] / [x ^ 2 (1 + x ^ 2)] DX?

Do two definite integrals with the same integral interval and integrand function be equal?
A. Equal  X05  x05b. Differ by an infinitesimal  X05  x05c. Differ by a constant  X05  x05d. Differ by any constant

A: Equal;
Let f (x) be an original function of F (x);
Since the integral interval is the same, let [a, b]
Then: integral result = f (b) + C - (f (a) + C) = f (b) - f (a);

If the school wants to decorate a meeting room, it needs 600 pieces of square bricks with a side length of 3 decimeters; if it wants to use square bricks with a side length of 5 decimeters, how many bricks do it need? (solve by proportion)

Suppose that x bricks are needed if the floor is paved with square bricks with side length of 5 decimeters, then: (5 × 5) x = (3 × 3) × 600, & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; X = 216; a: if the floor is paved with square bricks with side length of 5 decimeters, 216 bricks are required

The reduction ratio is 4 / 7; 2 / 7, 15 / 2; 2 / 12, 2 / 2; 1 / 3, 15 / 21, 6 / 1; 9 / 4, 1 / 5; 4 / 4, 81; 4.51.25; 2 / 2, 18 / 6; 2 / 10.9; 5 / 3, 7.2; 9 / 1.2; 48, 12 / 1; 18 / 1; 0.03, 1.2; 36, 4 / 1; 8 / 1. Help me finish it before 12:00

4 of 7; 2 of 7 = 2:1, 2 of 15; 2 of 12 = 4:5, 1 of 2; 1 of 3 = 3:2, 21 of 15 = 7:5, 1 of 6; 4 of 9 = 3:8, 1 of 5; 3 of 4 = 8:5, 81 of 4; 4.5 = 18:1, 1.25; 1 of 2 = 1:2, 8 of 6; 1 of 2 = 3:20.9; 3 of 5 = 3:27.2; 9 = 4:5, 1.2; 48 =

If Π / 2 ＜ B ＜ 3 Π / 4, cos (a-b) = 12 / 13, sin (a + b) = - 3 / 5, then sin2a =?

2A = A-B + A + B, according to cos (a-b) = 12 / 13, sin (a + b) = - 3 / 5
Sin (a-b), cos (a + b), then sin2a can be obtained

On the 11000 drawings, a square has an area of 16 square centimeters, and its actual area is______ Square meters

① Find the side length of the square on the graph: A2 = 16 (square centimeter); 16 is the square of 4; & nbsp; a = 4 (centimeter); ② find the actual side length of the square: 4 △ 11000 = 4 × 1000 = 4000 (centimeter); 4000cm = 40m; ③ find the actual area of the square: 40 × 40 = 1600 (square meter); answer: its actual area is 1600 square meter. So the answer is: 1600

Urgent! Help to do a few high school math problems! Online and other answers!
1. Let f (x) = the third power of x plus 2 times the square of x minus 4
2. When x = 2 / 3, y = FX has extremum
3. Find the monotone interval of FX and the maximum and minimum value of function on [3,1]

F(x)=x^3+2x^2-4
1.f'(x)=3x^2+4x
When x = 2 / 3, f '(x) = 0
Namely
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Find f (x) = x3-3x K, G (x) = (2kx-k) / (X22) y = x ^ 3x-2 find f (x) = x3-3x K, G (x) = (2kx-k) / (X22) y = x ^ 3x-2
Ax * 2 BX C = 0 medium AC

Y = (m-1) X2 (m-2) X-1 the affine line intersects at the point O, and f (x) = xlnx (A-1) x2y-x = 4

There are five identical rectangles to form a large rectangle with an area of 480 square centimeters. How many meters is the perimeter of the large rectangle?

Five identical rectangles make a big rectangle
A small rectangle is twice as long as it is wide
Let the width of the small rectangle be a
Large rectangle area = (2a + 2A + a) * 2A = 480
10a^2=480
A = 4 times root sign 3
The perimeter of the large rectangle = (2a + 2A + A + 2a) * 2 = 14a = 56 times the root sign 3 = 96.995, about 97 cm