Find the area of the region bounded by the graphs of the given equations.   y=4x−x2​, y=−3x The area is

Q: Differentiate. 3 3 y= Vx + 12x +4 -x y' D

A: y=x3+12x+43 ·x3y=x3+12x+413 ·x3y''=ddxx3+12x+413 ·x3…

Q: Find the area of the shaded region. y x = y -8 -6 -4 -2 4 Hy=-1 2.

A:

Q: Find the total area of the shaded region. 10- y = 8 6- 4- y=8 cosx 2- 1/2 元 Зл/2

A: Given curve y=8cos2x  liney=8

Q: The graph of y=15+2x – x is shown in the figure to the right. Find the area of the shaded region. 40…

A: First find the x intercept of the graph than integrate in that interval.

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.