28. Hypervolume We have learned that "1 dx is the length of the interval [a, b] on the number line (one-dimensional space), IR1 dA is the area of region R in the xy-plane (two-dimensional space), and ,1 dV is the volume of the region D in three- dimensional space (xyz-space). We could continue: If Q is a region in 4-space (xyzw-space), then .1 dV is the “hyper-volume" of Q. Use your generalizing abilities and a Cartesian coordinate system of 4-space to find the hypervolume inside the unit 4-dimensional sphere x² + y² + z? + w² = 1.

Q: Find the area of the plane region bounded by y=-x+2 and y=x²-2x 07 s.u. 9 9 s.u. 01 S.U. 2 S.U.

A:

Q: 3. Let R be the region below bounded by the parabola y = 4 - x² and the lines 3x-2y+3=0 and y = 0.…

A: Given that,  R be the region bounded by y=4-x2 and 3x-2y+3=0 and y=0. (a) Divided  the region in two…

Q: Find the of the region bounded by the parabolas y – 6x = -x² and y + 2x = x² , area

A:

Q: Find the area of the region(s) bounded by y = -x5-2x4 - x² +4 and y = 2x + 1

A:

Q: 4. Consider the rectangle bounded by x = 1 and x = 4 on the y-interval [3, 3.5]. (a) What is the…

A:

Q: Q2) A) Graph the curve Y = x (x +5)(x-3) between the value of x [-5, 3], then find the area of the…

A:

Q: Find the area of ​​the plane x + y + z = 6 in cylinder X² + y² = 4

A: According to the given information, it is required to find the area of the plane in the cylinder.

Q: Find the AREA and VOLUME (Identify what type of volume) bounded by the equations; y = 4x - x² and x…

A: The given curves are y=4x-x2 and x+y=4 We have to find the area and the volume bounded by these…

Q: 2. Find the area of the region bounded by y = 2x² +10, y = 4x+16, x = -2, and x = 5.

A: first draw bounded region then find limit of region and using vertical strips find the area

Q: Find the area of ​​region R bounded by y = 2x, y = 5x and y = 5 in the first quadrant  NOTE: The R…

A:

Q: x=cos¬! 1 prove that sec" X= cos

A: Given sec-1x=cos-11x