of variables (x² – y*) d A ere R the region is defined by the rectangular region that is enclosed the given lines of :y = 1 – x. , y = x, y = -x and y = x + 2.

Q: areas Region boundad by y=x y and y e2

A:

Q: Evaluate ſſ, Vy² – x² dA where boundary of R is the parallelogram bounded by the four lines

A: In this question, we evaluate the double integral by using the change of variable. The region is…

Q: The area bounded by the curve y3a and the lines z 4 and a-9 above the z-azis is aquare units O 27v0…

A:

Q: Use the indicated change of variables to evaluate ||. (xy+x²)dA. x=u, y=-(u-v), and R is the region…

A: By using the change of variable

Q: Let R be the rectangular region with (1,2) , (2,3) , (3,2) and (2,1) as corners. Use change of…

A: Changing the variables

Q: 1 Set up and evaluate , 6x dA, where R is the rectangular region with corners (-2, 0), (3,0), (-2,…

A:

Q: Find the areas of the regions enclosed by the lines and curves, y = x² - 2x and y = x yx728 3

A: Given curves are y = x2 - 2x and y = x

Q: Consider the region bounded by y = x² and y = 8. Find the number b so the line y = b divides this…

A:

Q: Find the area of the shaded region given below. y = √√√=x+4 y = √√x + 4 neg y = x² + 4 x = y² -6y +8…

A:

Q: 7. Find the are of the regions enclosed by the lines and curves. Draw graphs a) x = 2y², x = 0, y =…

A: We use integration with respect to y axis for part a  and with respect to x for part b

Q: 19. y² dA, D is the triangular region with vertices (0, 1), (1, 2), (4, 1)

A: 19. Given D is the triangular region with vertices (0, 1), (1, 2), (4, 1).We find the given double…

Q: The area of the region bounded by the curves y = 4x? 3 22 and the lines æ = 1 and x = 5 and y is

A: Here is the solution of the given problem

Q: Find and describe the region inscribed by the lines (x-axis), (y = -x+2) and (x = 2y-4) under the…

A:

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.