5. Find the area of the region. (a) y = sinx, y = x, x = π/2, x = π (b) x = 1 - y², x = y² – 1 (c) 4x + y² = 12, x = y

Q: 29) Find the area bounded by the curves y= In x, y = 2 In x and line x-e in the first quadrant.

A: I have given the answer in the next step. Hope you understand that

Q: Find y SX a) y = 3 sin (x² + 5x - 3) y' = c) y = sin" (6x) y'= b) xE5X+2 d) y = In (2x) Y₁ = Y y' =

A:

Q: I the total area bounded

A: Here we have to find the area bounded by the curves

Q: Consider the functions y₁(x) = x - 2 and y2(x) = (x - 2)². (A) Find analytically the intersection…

A:

Q: (b) the curve x = = y²-y-6 and the line x = = 2y + 4;

A: Given; x=y^2-y-6, x=2y+4

Q: Find the area enclosed a'x = y°(2a – y)| 2 X. -

A:

Q: y = x - 15 x 10 y = x (4, 4) -6 -4 4 K-4,-4) - 10 - 20 20

A:

Q: (c) curve y = 5-x", line y=x+3 (d) y= sinx, y=cosx, x= 7 /4, x=7/2

A: Double integers

Q: Find the area bounded by the parabolas (x-3)² - 16ky = 0 and y² - 16k (x-3) = 0.

A:

Q: Which integral corresponds to the area of the shaded region? The parabola is y = x? –1 while the…

A: Given query is to find the the integral for the area of shaded region.

Q: Find the area of the region between the curve y = 3 - x² and the line y = 1 -x from x = 0 and x = 2.…

A: The region between the curve y=3-x2 and the line y=1-x from x=0 to x=2